Non-perturbative methods in 2 dimensional quantum field theory /:
The second edition of Non-Perturbative Methods in Two-Dimensional Quantum Field Theory is an extensively revised version, involving major changes and additions. Although much of the material is special to two dimensions, the techniques used should prove helpful also in the development of techniques...
Gespeichert in:
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| Weitere Verfasser: | , |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore ; River Edge, NJ :
World Scientific,
©2001.
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| Ausgabe: | 2nd ed. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | The second edition of Non-Perturbative Methods in Two-Dimensional Quantum Field Theory is an extensively revised version, involving major changes and additions. Although much of the material is special to two dimensions, the techniques used should prove helpful also in the development of techniques applicable in higher dimensions. In particular, the last three chapters of the book will be of direct interest to researchers wanting to work in the field of conformal field theory and strings. This book is intended for students working for their PhD degree and post-doctoral researchers wishing to a. |
| Beschreibung: | 1 online resource (832 pages) : illustrations |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9789812810151 9812810153 1281951676 9781281951670 9786611951672 6611951679 |
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| 245 | 1 | 0 | |a Non-perturbative methods in 2 dimensional quantum field theory / |c Elcio Abdalla, M. Cristina B. Abdalla, Klaus D. Rothe. |
| 246 | 3 | 0 | |a 2 dimensional quantum field theory |
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| 520 | |a The second edition of Non-Perturbative Methods in Two-Dimensional Quantum Field Theory is an extensively revised version, involving major changes and additions. Although much of the material is special to two dimensions, the techniques used should prove helpful also in the development of techniques applicable in higher dimensions. In particular, the last three chapters of the book will be of direct interest to researchers wanting to work in the field of conformal field theory and strings. This book is intended for students working for their PhD degree and post-doctoral researchers wishing to a. | ||
| 505 | 0 | |a 1. Introduction -- 2. Free fields. 2.1. Introduction. 2.2. Bosonic free fields. 2.3. Fermionic free fields. 2.4. Bosonization of massless fermions. 2.5. The RS-model. 2.6. Conclusions -- 3. The Thirring model. 3.1. Introduction. 3.2. The massless Thirring model. 3.3. The massive Thirring model. 3.4. Bosonization revisited. 3.5. The soliton as a disorder parameter. 3.6. Conclusion -- 4. Determinants and heat kernels. 4.1. Introduction. 4.2. Functional determinant, one-loop diagram. 4.3. Calculating Seeley coefficients. 4.4. Computing functional determinants. 4.5. A theorem on a one parameter family of factorizable operators. 4.6. The QCD2 functional determinant. 4.7. Zero-modes. 4.8. Ambiguities in functional determinants. 4.9. Mass expansion in proper-time regularization. 4.10. The finite temperature heat kernel. 4.11. Conclusion -- 5. Self-interacting fermionic models. 5.1. Introduction. 5.2. The O(N) invariant Gross-Neveu model. 5.3. Chiral Gross-Neveu model. 5.4. Conclusions and physical interpretation -- 6. Non-linear [symbol] models: Classical aspects. 6.1. Historical development. 6.2. Sigma models and current algebra. 6.3. Two-dimensional [symbol] models: preliminaries. 6.4. Purely bosonic non-linear a models. 6.5. Non-linear [symbol] models with fermions. 6.6. Analogies with 4D gauge theories. 6.7. Concluding remarks -- 7. Non-linear [symbol] models -- Quantum aspects. 7.1. Introduction. 7.2. Grassmannian bosonic models. 7.3. Grassmannian models and fermions. 7.4. Quantization of higher conservation laws. 7.5. Algebra of non-local charges. 7.6. Non-local charges in the WZNW model. 7.7. Perturbative renormalization. 7.8. Anomalous non-linear [symbol] models in four dimensions. 7.9. Conclusion -- 8. Exact S-matrices of 2D models. 8.1. Introduction. 8.2. S-matrices and conservation laws. 8.3. Quantum non-local charges and S-matrices. 8.4. Boundary S-matrices. 8.5. Further developments. 8.6. Conclusion -- 9. The Wess-Zumino-Witten theory. 9.1. Introduction. 9.2. Existence of a critical point. 9.3. Properties at the critical point. 9.4. Properties off the critical point. 9.5. Conclusion -- 10. QED2: Operator approach. 10.1. Introduction. 10.2. The Massless Schwinger model. 10.3. The Massive Schwinger model. 10.4. Conclusion -- 11. Quantum chromodynamics. 11.1. Introduction. 11.2. The 1/N expansion: 't Hooft model. 11.3. Currents, Green functions and determinants. 11.4. Local decoupled formulation and BRST constraints. 11.5. Non-local decoupled formulation and BRST constraints. 11.6. The physical Hilbert space. 11.7. The QCD2 vacuum. 11.8. Massive two-dimensional QCD. 11.9. Screening in two-dimensional QCD. ll.lO. Further algebraic aspects. 11.11. Conclusions -- 12. QED2: Functional approach. 12.1. Introduction. 12.2. Equivalent bosonic action. 12.3. Gauge invariant correlation functions. 12.4. Vacuum structure. 12.5. Why study gauge-invariant correlators. 12.6. Screening versus confinement. 12.7. Quasi-periodic boundary conditions and the [symbol]-vacuum. 12.8. Axial anomaly and the Dirac sea. 12.9. Functional representation of tunneling amplitudes. 12.10. Interpretation of the result. 12.11. Eigenvalue spectrum of the Dirac operator. 12.12. Zero modes and boundary-value problem. 12.13. The U(l) problem revisited. 12.14. Conclusion -- 13. The finite temperature Schwinger model. 13.1. Introduction. 13.2. Heat kernel and Seeley expansion. 13.3. The Atiyah-Singer index theorem. 13.4. Fermions in an instanton potential. 13.5. Chiral condensate and symmetry breaking. 13.6. Polyakov loop-operator and screening. 13.7. Conclusion -- 14. Non-abelian chiral gauge theories. 14.1. Introduction. 14.2. Anomalies and cocycles. 14.3. Isomorphic representations of chiral QCD2. 14.4. Constraint structure from the fermionic Hamiltonian. 14.5. Chiral QCD2 in the local decoupled formulation. 14.6. Conclusion -- 15. Chiral quantum electrodynamics. 15.1. Introduction. 15.2. The JR model. 15.3. Quantization in the GNI formulation. 15.4. Quantization in the GI formulation. 15.5. Path-integral formulation. 15.6. Perturbative analysis in the fermionic formulation. 15.7. Anomalous poisson brackets revisited. 15.8. Chiral QED2 in terms of chiral bosons. 15.9. Conclusion -- 16. Conformally invariant field theory. 16.1. Introduction. 16.2. Conformal transformations and conformal group. 16.3. The conformal group in two dimensions. 16.4. The BPZ construction. 16.5. Realization of conformal algebra for c <1. 16.6. Superconformal symmetry. 16.7. Conclusion -- 17. Conformal field theory with internal symmetry. 17.1. Introduction. 17.2. Conformal algebra and Ward identities. 17.3. Realizations of non-Abelian conformal algebra. 17.4. Coset description of CQFT. 17.5. Critical statistical models. 17.6. Conclusions -- 18. 2D gravity and string related topics. 18.1. Introduction. 18.2. The Nambu-Goto string. 18.3. The effective action of 2D quantum gravity. 18.4. The Liouville theory. 18.5. Gravity in the light-cone gauge. 18.6. Conclusion -- 19. Final remarks. | |
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| contents | 1. Introduction -- 2. Free fields. 2.1. Introduction. 2.2. Bosonic free fields. 2.3. Fermionic free fields. 2.4. Bosonization of massless fermions. 2.5. The RS-model. 2.6. Conclusions -- 3. The Thirring model. 3.1. Introduction. 3.2. The massless Thirring model. 3.3. The massive Thirring model. 3.4. Bosonization revisited. 3.5. The soliton as a disorder parameter. 3.6. Conclusion -- 4. Determinants and heat kernels. 4.1. Introduction. 4.2. Functional determinant, one-loop diagram. 4.3. Calculating Seeley coefficients. 4.4. Computing functional determinants. 4.5. A theorem on a one parameter family of factorizable operators. 4.6. The QCD2 functional determinant. 4.7. Zero-modes. 4.8. Ambiguities in functional determinants. 4.9. Mass expansion in proper-time regularization. 4.10. The finite temperature heat kernel. 4.11. Conclusion -- 5. Self-interacting fermionic models. 5.1. Introduction. 5.2. The O(N) invariant Gross-Neveu model. 5.3. Chiral Gross-Neveu model. 5.4. Conclusions and physical interpretation -- 6. Non-linear [symbol] models: Classical aspects. 6.1. Historical development. 6.2. Sigma models and current algebra. 6.3. Two-dimensional [symbol] models: preliminaries. 6.4. Purely bosonic non-linear a models. 6.5. Non-linear [symbol] models with fermions. 6.6. Analogies with 4D gauge theories. 6.7. Concluding remarks -- 7. Non-linear [symbol] models -- Quantum aspects. 7.1. Introduction. 7.2. Grassmannian bosonic models. 7.3. Grassmannian models and fermions. 7.4. Quantization of higher conservation laws. 7.5. Algebra of non-local charges. 7.6. Non-local charges in the WZNW model. 7.7. Perturbative renormalization. 7.8. Anomalous non-linear [symbol] models in four dimensions. 7.9. Conclusion -- 8. Exact S-matrices of 2D models. 8.1. Introduction. 8.2. S-matrices and conservation laws. 8.3. Quantum non-local charges and S-matrices. 8.4. Boundary S-matrices. 8.5. Further developments. 8.6. Conclusion -- 9. The Wess-Zumino-Witten theory. 9.1. Introduction. 9.2. Existence of a critical point. 9.3. Properties at the critical point. 9.4. Properties off the critical point. 9.5. Conclusion -- 10. QED2: Operator approach. 10.1. Introduction. 10.2. The Massless Schwinger model. 10.3. The Massive Schwinger model. 10.4. Conclusion -- 11. Quantum chromodynamics. 11.1. Introduction. 11.2. The 1/N expansion: 't Hooft model. 11.3. Currents, Green functions and determinants. 11.4. Local decoupled formulation and BRST constraints. 11.5. Non-local decoupled formulation and BRST constraints. 11.6. The physical Hilbert space. 11.7. The QCD2 vacuum. 11.8. Massive two-dimensional QCD. 11.9. Screening in two-dimensional QCD. ll.lO. Further algebraic aspects. 11.11. Conclusions -- 12. QED2: Functional approach. 12.1. Introduction. 12.2. Equivalent bosonic action. 12.3. Gauge invariant correlation functions. 12.4. Vacuum structure. 12.5. Why study gauge-invariant correlators. 12.6. Screening versus confinement. 12.7. Quasi-periodic boundary conditions and the [symbol]-vacuum. 12.8. Axial anomaly and the Dirac sea. 12.9. Functional representation of tunneling amplitudes. 12.10. Interpretation of the result. 12.11. Eigenvalue spectrum of the Dirac operator. 12.12. Zero modes and boundary-value problem. 12.13. The U(l) problem revisited. 12.14. Conclusion -- 13. The finite temperature Schwinger model. 13.1. Introduction. 13.2. Heat kernel and Seeley expansion. 13.3. The Atiyah-Singer index theorem. 13.4. Fermions in an instanton potential. 13.5. Chiral condensate and symmetry breaking. 13.6. Polyakov loop-operator and screening. 13.7. Conclusion -- 14. Non-abelian chiral gauge theories. 14.1. Introduction. 14.2. Anomalies and cocycles. 14.3. Isomorphic representations of chiral QCD2. 14.4. Constraint structure from the fermionic Hamiltonian. 14.5. Chiral QCD2 in the local decoupled formulation. 14.6. Conclusion -- 15. Chiral quantum electrodynamics. 15.1. Introduction. 15.2. The JR model. 15.3. Quantization in the GNI formulation. 15.4. Quantization in the GI formulation. 15.5. Path-integral formulation. 15.6. Perturbative analysis in the fermionic formulation. 15.7. Anomalous poisson brackets revisited. 15.8. Chiral QED2 in terms of chiral bosons. 15.9. Conclusion -- 16. Conformally invariant field theory. 16.1. Introduction. 16.2. Conformal transformations and conformal group. 16.3. The conformal group in two dimensions. 16.4. The BPZ construction. 16.5. Realization of conformal algebra for c <1. 16.6. Superconformal symmetry. 16.7. Conclusion -- 17. Conformal field theory with internal symmetry. 17.1. Introduction. 17.2. Conformal algebra and Ward identities. 17.3. Realizations of non-Abelian conformal algebra. 17.4. Coset description of CQFT. 17.5. Critical statistical models. 17.6. Conclusions -- 18. 2D gravity and string related topics. 18.1. Introduction. 18.2. The Nambu-Goto string. 18.3. The effective action of 2D quantum gravity. 18.4. The Liouville theory. 18.5. Gravity in the light-cone gauge. 18.6. Conclusion -- 19. Final remarks. |
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Although much of the material is special to two dimensions, the techniques used should prove helpful also in the development of techniques applicable in higher dimensions. In particular, the last three chapters of the book will be of direct interest to researchers wanting to work in the field of conformal field theory and strings. This book is intended for students working for their PhD degree and post-doctoral researchers wishing to a.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">1. Introduction -- 2. Free fields. 2.1. Introduction. 2.2. Bosonic free fields. 2.3. Fermionic free fields. 2.4. Bosonization of massless fermions. 2.5. The RS-model. 2.6. Conclusions -- 3. The Thirring model. 3.1. Introduction. 3.2. The massless Thirring model. 3.3. The massive Thirring model. 3.4. Bosonization revisited. 3.5. The soliton as a disorder parameter. 3.6. Conclusion -- 4. Determinants and heat kernels. 4.1. Introduction. 4.2. Functional determinant, one-loop diagram. 4.3. Calculating Seeley coefficients. 4.4. Computing functional determinants. 4.5. A theorem on a one parameter family of factorizable operators. 4.6. The QCD2 functional determinant. 4.7. Zero-modes. 4.8. Ambiguities in functional determinants. 4.9. Mass expansion in proper-time regularization. 4.10. The finite temperature heat kernel. 4.11. Conclusion -- 5. Self-interacting fermionic models. 5.1. Introduction. 5.2. The O(N) invariant Gross-Neveu model. 5.3. Chiral Gross-Neveu model. 5.4. Conclusions and physical interpretation -- 6. Non-linear [symbol] models: Classical aspects. 6.1. Historical development. 6.2. Sigma models and current algebra. 6.3. Two-dimensional [symbol] models: preliminaries. 6.4. Purely bosonic non-linear a models. 6.5. Non-linear [symbol] models with fermions. 6.6. Analogies with 4D gauge theories. 6.7. Concluding remarks -- 7. Non-linear [symbol] models -- Quantum aspects. 7.1. Introduction. 7.2. Grassmannian bosonic models. 7.3. Grassmannian models and fermions. 7.4. Quantization of higher conservation laws. 7.5. Algebra of non-local charges. 7.6. Non-local charges in the WZNW model. 7.7. Perturbative renormalization. 7.8. Anomalous non-linear [symbol] models in four dimensions. 7.9. Conclusion -- 8. Exact S-matrices of 2D models. 8.1. Introduction. 8.2. S-matrices and conservation laws. 8.3. Quantum non-local charges and S-matrices. 8.4. Boundary S-matrices. 8.5. Further developments. 8.6. Conclusion -- 9. The Wess-Zumino-Witten theory. 9.1. Introduction. 9.2. Existence of a critical point. 9.3. Properties at the critical point. 9.4. Properties off the critical point. 9.5. Conclusion -- 10. QED2: Operator approach. 10.1. Introduction. 10.2. The Massless Schwinger model. 10.3. The Massive Schwinger model. 10.4. Conclusion -- 11. Quantum chromodynamics. 11.1. Introduction. 11.2. The 1/N expansion: 't Hooft model. 11.3. Currents, Green functions and determinants. 11.4. Local decoupled formulation and BRST constraints. 11.5. Non-local decoupled formulation and BRST constraints. 11.6. The physical Hilbert space. 11.7. The QCD2 vacuum. 11.8. Massive two-dimensional QCD. 11.9. Screening in two-dimensional QCD. ll.lO. Further algebraic aspects. 11.11. Conclusions -- 12. QED2: Functional approach. 12.1. Introduction. 12.2. Equivalent bosonic action. 12.3. Gauge invariant correlation functions. 12.4. Vacuum structure. 12.5. Why study gauge-invariant correlators. 12.6. Screening versus confinement. 12.7. Quasi-periodic boundary conditions and the [symbol]-vacuum. 12.8. Axial anomaly and the Dirac sea. 12.9. Functional representation of tunneling amplitudes. 12.10. Interpretation of the result. 12.11. Eigenvalue spectrum of the Dirac operator. 12.12. Zero modes and boundary-value problem. 12.13. The U(l) problem revisited. 12.14. Conclusion -- 13. The finite temperature Schwinger model. 13.1. Introduction. 13.2. Heat kernel and Seeley expansion. 13.3. The Atiyah-Singer index theorem. 13.4. Fermions in an instanton potential. 13.5. Chiral condensate and symmetry breaking. 13.6. Polyakov loop-operator and screening. 13.7. Conclusion -- 14. Non-abelian chiral gauge theories. 14.1. Introduction. 14.2. Anomalies and cocycles. 14.3. Isomorphic representations of chiral QCD2. 14.4. Constraint structure from the fermionic Hamiltonian. 14.5. Chiral QCD2 in the local decoupled formulation. 14.6. Conclusion -- 15. Chiral quantum electrodynamics. 15.1. Introduction. 15.2. The JR model. 15.3. Quantization in the GNI formulation. 15.4. Quantization in the GI formulation. 15.5. Path-integral formulation. 15.6. Perturbative analysis in the fermionic formulation. 15.7. Anomalous poisson brackets revisited. 15.8. Chiral QED2 in terms of chiral bosons. 15.9. Conclusion -- 16. Conformally invariant field theory. 16.1. Introduction. 16.2. Conformal transformations and conformal group. 16.3. The conformal group in two dimensions. 16.4. The BPZ construction. 16.5. Realization of conformal algebra for c <1. 16.6. Superconformal symmetry. 16.7. Conclusion -- 17. Conformal field theory with internal symmetry. 17.1. Introduction. 17.2. Conformal algebra and Ward identities. 17.3. Realizations of non-Abelian conformal algebra. 17.4. Coset description of CQFT. 17.5. Critical statistical models. 17.6. Conclusions -- 18. 2D gravity and string related topics. 18.1. Introduction. 18.2. The Nambu-Goto string. 18.3. The effective action of 2D quantum gravity. 18.4. The Liouville theory. 18.5. Gravity in the light-cone gauge. 18.6. Conclusion -- 19. Final remarks.</subfield></datafield><datafield tag="546" ind1=" " ind2=" "><subfield code="a">English.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Quantum field theory</subfield><subfield code="x">Mathematical models.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Théorie quantique des champs</subfield><subfield code="x">Modèles mathématiques.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">SCIENCE</subfield><subfield code="x">Waves & Wave Mechanics.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Quantum field theory</subfield><subfield code="x">Mathematical models</subfield><subfield code="2">fast</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Abdalla, M. Cristina B.</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCjFDQpPQwjjFMwgb4GXdjP</subfield><subfield code="0">http://id.loc.gov/authorities/names/n91071635</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Rothe, Klaus D.</subfield><subfield code="q">(Klaus Dieter)</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCjKPgqRvD98kmRf7g9crjd</subfield><subfield code="0">http://id.loc.gov/authorities/names/n91071653</subfield></datafield><datafield tag="758" ind1=" " ind2=" "><subfield code="i">has work:</subfield><subfield code="a">Non-perturbative methods in 2 dimensional quantum field theory (Text)</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCGdTgjvFKrH8W6PjXdYVYd</subfield><subfield code="4">https://id.oclc.org/worldcat/ontology/hasWork</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Abdalla, Elcio.</subfield><subfield code="t">Non-perturbative methods in 2 dimensional quantum field theory.</subfield><subfield code="b">2nd ed.</subfield><subfield code="d">Singapore ; River Edge, NJ : World Scientific, ©2001</subfield><subfield code="z">9810245963</subfield><subfield code="z">9789810245962</subfield><subfield code="w">(DLC) 2001278446</subfield><subfield code="w">(OCoLC)48256841</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235841</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts Library Services</subfield><subfield code="b">ASKH</subfield><subfield code="n">AH24685524</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ProQuest Ebook Central</subfield><subfield code="b">EBLB</subfield><subfield code="n">EBL1681657</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ebrary</subfield><subfield code="b">EBRY</subfield><subfield code="n">ebr10255905</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">235841</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">2901913</subfield></datafield><datafield tag="994" ind1=" " ind2=" "><subfield code="a">92</subfield><subfield code="b">GEBAY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-863</subfield></datafield></record></collection> |
| id | ZDB-4-EBA-ocn271427415 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:16:34Z |
| institution | BVB |
| isbn | 9789812810151 9812810153 1281951676 9781281951670 9786611951672 6611951679 |
| language | English |
| oclc_num | 271427415 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (832 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | World Scientific, |
| record_format | marc |
| spelling | Abdalla, Elcio. https://id.oclc.org/worldcat/entity/E39PBJv8GpMkPgbgY34tgpqbBP http://id.loc.gov/authorities/names/n91071623 Non-perturbative methods in 2 dimensional quantum field theory / Elcio Abdalla, M. Cristina B. Abdalla, Klaus D. Rothe. 2 dimensional quantum field theory 2nd ed. Singapore ; River Edge, NJ : World Scientific, ©2001. 1 online resource (832 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references and index. Print version record. The second edition of Non-Perturbative Methods in Two-Dimensional Quantum Field Theory is an extensively revised version, involving major changes and additions. Although much of the material is special to two dimensions, the techniques used should prove helpful also in the development of techniques applicable in higher dimensions. In particular, the last three chapters of the book will be of direct interest to researchers wanting to work in the field of conformal field theory and strings. This book is intended for students working for their PhD degree and post-doctoral researchers wishing to a. 1. Introduction -- 2. Free fields. 2.1. Introduction. 2.2. Bosonic free fields. 2.3. Fermionic free fields. 2.4. Bosonization of massless fermions. 2.5. The RS-model. 2.6. Conclusions -- 3. The Thirring model. 3.1. Introduction. 3.2. The massless Thirring model. 3.3. The massive Thirring model. 3.4. Bosonization revisited. 3.5. The soliton as a disorder parameter. 3.6. Conclusion -- 4. Determinants and heat kernels. 4.1. Introduction. 4.2. Functional determinant, one-loop diagram. 4.3. Calculating Seeley coefficients. 4.4. Computing functional determinants. 4.5. A theorem on a one parameter family of factorizable operators. 4.6. The QCD2 functional determinant. 4.7. Zero-modes. 4.8. Ambiguities in functional determinants. 4.9. Mass expansion in proper-time regularization. 4.10. The finite temperature heat kernel. 4.11. Conclusion -- 5. Self-interacting fermionic models. 5.1. Introduction. 5.2. The O(N) invariant Gross-Neveu model. 5.3. Chiral Gross-Neveu model. 5.4. Conclusions and physical interpretation -- 6. Non-linear [symbol] models: Classical aspects. 6.1. Historical development. 6.2. Sigma models and current algebra. 6.3. Two-dimensional [symbol] models: preliminaries. 6.4. Purely bosonic non-linear a models. 6.5. Non-linear [symbol] models with fermions. 6.6. Analogies with 4D gauge theories. 6.7. Concluding remarks -- 7. Non-linear [symbol] models -- Quantum aspects. 7.1. Introduction. 7.2. Grassmannian bosonic models. 7.3. Grassmannian models and fermions. 7.4. Quantization of higher conservation laws. 7.5. Algebra of non-local charges. 7.6. Non-local charges in the WZNW model. 7.7. Perturbative renormalization. 7.8. Anomalous non-linear [symbol] models in four dimensions. 7.9. Conclusion -- 8. Exact S-matrices of 2D models. 8.1. Introduction. 8.2. S-matrices and conservation laws. 8.3. Quantum non-local charges and S-matrices. 8.4. Boundary S-matrices. 8.5. Further developments. 8.6. Conclusion -- 9. The Wess-Zumino-Witten theory. 9.1. Introduction. 9.2. Existence of a critical point. 9.3. Properties at the critical point. 9.4. Properties off the critical point. 9.5. Conclusion -- 10. QED2: Operator approach. 10.1. Introduction. 10.2. The Massless Schwinger model. 10.3. The Massive Schwinger model. 10.4. Conclusion -- 11. Quantum chromodynamics. 11.1. Introduction. 11.2. The 1/N expansion: 't Hooft model. 11.3. Currents, Green functions and determinants. 11.4. Local decoupled formulation and BRST constraints. 11.5. Non-local decoupled formulation and BRST constraints. 11.6. The physical Hilbert space. 11.7. The QCD2 vacuum. 11.8. Massive two-dimensional QCD. 11.9. Screening in two-dimensional QCD. ll.lO. Further algebraic aspects. 11.11. Conclusions -- 12. QED2: Functional approach. 12.1. Introduction. 12.2. Equivalent bosonic action. 12.3. Gauge invariant correlation functions. 12.4. Vacuum structure. 12.5. Why study gauge-invariant correlators. 12.6. Screening versus confinement. 12.7. Quasi-periodic boundary conditions and the [symbol]-vacuum. 12.8. Axial anomaly and the Dirac sea. 12.9. Functional representation of tunneling amplitudes. 12.10. Interpretation of the result. 12.11. Eigenvalue spectrum of the Dirac operator. 12.12. Zero modes and boundary-value problem. 12.13. The U(l) problem revisited. 12.14. Conclusion -- 13. The finite temperature Schwinger model. 13.1. Introduction. 13.2. Heat kernel and Seeley expansion. 13.3. The Atiyah-Singer index theorem. 13.4. Fermions in an instanton potential. 13.5. Chiral condensate and symmetry breaking. 13.6. Polyakov loop-operator and screening. 13.7. Conclusion -- 14. Non-abelian chiral gauge theories. 14.1. Introduction. 14.2. Anomalies and cocycles. 14.3. Isomorphic representations of chiral QCD2. 14.4. Constraint structure from the fermionic Hamiltonian. 14.5. Chiral QCD2 in the local decoupled formulation. 14.6. Conclusion -- 15. Chiral quantum electrodynamics. 15.1. Introduction. 15.2. The JR model. 15.3. Quantization in the GNI formulation. 15.4. Quantization in the GI formulation. 15.5. Path-integral formulation. 15.6. Perturbative analysis in the fermionic formulation. 15.7. Anomalous poisson brackets revisited. 15.8. Chiral QED2 in terms of chiral bosons. 15.9. Conclusion -- 16. Conformally invariant field theory. 16.1. Introduction. 16.2. Conformal transformations and conformal group. 16.3. The conformal group in two dimensions. 16.4. The BPZ construction. 16.5. Realization of conformal algebra for c <1. 16.6. Superconformal symmetry. 16.7. Conclusion -- 17. Conformal field theory with internal symmetry. 17.1. Introduction. 17.2. Conformal algebra and Ward identities. 17.3. Realizations of non-Abelian conformal algebra. 17.4. Coset description of CQFT. 17.5. Critical statistical models. 17.6. Conclusions -- 18. 2D gravity and string related topics. 18.1. Introduction. 18.2. The Nambu-Goto string. 18.3. The effective action of 2D quantum gravity. 18.4. The Liouville theory. 18.5. Gravity in the light-cone gauge. 18.6. Conclusion -- 19. Final remarks. English. Quantum field theory Mathematical models. Théorie quantique des champs Modèles mathématiques. SCIENCE Waves & Wave Mechanics. bisacsh Quantum field theory Mathematical models fast Abdalla, M. Cristina B. https://id.oclc.org/worldcat/entity/E39PCjFDQpPQwjjFMwgb4GXdjP http://id.loc.gov/authorities/names/n91071635 Rothe, Klaus D. (Klaus Dieter) https://id.oclc.org/worldcat/entity/E39PCjKPgqRvD98kmRf7g9crjd http://id.loc.gov/authorities/names/n91071653 has work: Non-perturbative methods in 2 dimensional quantum field theory (Text) https://id.oclc.org/worldcat/entity/E39PCGdTgjvFKrH8W6PjXdYVYd https://id.oclc.org/worldcat/ontology/hasWork Print version: Abdalla, Elcio. Non-perturbative methods in 2 dimensional quantum field theory. 2nd ed. Singapore ; River Edge, NJ : World Scientific, ©2001 9810245963 9789810245962 (DLC) 2001278446 (OCoLC)48256841 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235841 Volltext |
| spellingShingle | Abdalla, Elcio Non-perturbative methods in 2 dimensional quantum field theory / 1. Introduction -- 2. Free fields. 2.1. Introduction. 2.2. Bosonic free fields. 2.3. Fermionic free fields. 2.4. Bosonization of massless fermions. 2.5. The RS-model. 2.6. Conclusions -- 3. The Thirring model. 3.1. Introduction. 3.2. The massless Thirring model. 3.3. The massive Thirring model. 3.4. Bosonization revisited. 3.5. The soliton as a disorder parameter. 3.6. Conclusion -- 4. Determinants and heat kernels. 4.1. Introduction. 4.2. Functional determinant, one-loop diagram. 4.3. Calculating Seeley coefficients. 4.4. Computing functional determinants. 4.5. A theorem on a one parameter family of factorizable operators. 4.6. The QCD2 functional determinant. 4.7. Zero-modes. 4.8. Ambiguities in functional determinants. 4.9. Mass expansion in proper-time regularization. 4.10. The finite temperature heat kernel. 4.11. Conclusion -- 5. Self-interacting fermionic models. 5.1. Introduction. 5.2. The O(N) invariant Gross-Neveu model. 5.3. Chiral Gross-Neveu model. 5.4. Conclusions and physical interpretation -- 6. Non-linear [symbol] models: Classical aspects. 6.1. Historical development. 6.2. Sigma models and current algebra. 6.3. Two-dimensional [symbol] models: preliminaries. 6.4. Purely bosonic non-linear a models. 6.5. Non-linear [symbol] models with fermions. 6.6. Analogies with 4D gauge theories. 6.7. Concluding remarks -- 7. Non-linear [symbol] models -- Quantum aspects. 7.1. Introduction. 7.2. Grassmannian bosonic models. 7.3. Grassmannian models and fermions. 7.4. Quantization of higher conservation laws. 7.5. Algebra of non-local charges. 7.6. Non-local charges in the WZNW model. 7.7. Perturbative renormalization. 7.8. Anomalous non-linear [symbol] models in four dimensions. 7.9. Conclusion -- 8. Exact S-matrices of 2D models. 8.1. Introduction. 8.2. S-matrices and conservation laws. 8.3. Quantum non-local charges and S-matrices. 8.4. Boundary S-matrices. 8.5. Further developments. 8.6. Conclusion -- 9. The Wess-Zumino-Witten theory. 9.1. Introduction. 9.2. Existence of a critical point. 9.3. Properties at the critical point. 9.4. Properties off the critical point. 9.5. Conclusion -- 10. QED2: Operator approach. 10.1. Introduction. 10.2. The Massless Schwinger model. 10.3. The Massive Schwinger model. 10.4. Conclusion -- 11. Quantum chromodynamics. 11.1. Introduction. 11.2. The 1/N expansion: 't Hooft model. 11.3. Currents, Green functions and determinants. 11.4. Local decoupled formulation and BRST constraints. 11.5. Non-local decoupled formulation and BRST constraints. 11.6. The physical Hilbert space. 11.7. The QCD2 vacuum. 11.8. Massive two-dimensional QCD. 11.9. Screening in two-dimensional QCD. ll.lO. Further algebraic aspects. 11.11. Conclusions -- 12. QED2: Functional approach. 12.1. Introduction. 12.2. Equivalent bosonic action. 12.3. Gauge invariant correlation functions. 12.4. Vacuum structure. 12.5. Why study gauge-invariant correlators. 12.6. Screening versus confinement. 12.7. Quasi-periodic boundary conditions and the [symbol]-vacuum. 12.8. Axial anomaly and the Dirac sea. 12.9. Functional representation of tunneling amplitudes. 12.10. Interpretation of the result. 12.11. Eigenvalue spectrum of the Dirac operator. 12.12. Zero modes and boundary-value problem. 12.13. The U(l) problem revisited. 12.14. Conclusion -- 13. The finite temperature Schwinger model. 13.1. Introduction. 13.2. Heat kernel and Seeley expansion. 13.3. The Atiyah-Singer index theorem. 13.4. Fermions in an instanton potential. 13.5. Chiral condensate and symmetry breaking. 13.6. Polyakov loop-operator and screening. 13.7. Conclusion -- 14. Non-abelian chiral gauge theories. 14.1. Introduction. 14.2. Anomalies and cocycles. 14.3. Isomorphic representations of chiral QCD2. 14.4. Constraint structure from the fermionic Hamiltonian. 14.5. Chiral QCD2 in the local decoupled formulation. 14.6. Conclusion -- 15. Chiral quantum electrodynamics. 15.1. Introduction. 15.2. The JR model. 15.3. Quantization in the GNI formulation. 15.4. Quantization in the GI formulation. 15.5. Path-integral formulation. 15.6. Perturbative analysis in the fermionic formulation. 15.7. Anomalous poisson brackets revisited. 15.8. Chiral QED2 in terms of chiral bosons. 15.9. Conclusion -- 16. Conformally invariant field theory. 16.1. Introduction. 16.2. Conformal transformations and conformal group. 16.3. The conformal group in two dimensions. 16.4. The BPZ construction. 16.5. Realization of conformal algebra for c <1. 16.6. Superconformal symmetry. 16.7. Conclusion -- 17. Conformal field theory with internal symmetry. 17.1. Introduction. 17.2. Conformal algebra and Ward identities. 17.3. Realizations of non-Abelian conformal algebra. 17.4. Coset description of CQFT. 17.5. Critical statistical models. 17.6. Conclusions -- 18. 2D gravity and string related topics. 18.1. Introduction. 18.2. The Nambu-Goto string. 18.3. The effective action of 2D quantum gravity. 18.4. The Liouville theory. 18.5. Gravity in the light-cone gauge. 18.6. Conclusion -- 19. Final remarks. Quantum field theory Mathematical models. Théorie quantique des champs Modèles mathématiques. SCIENCE Waves & Wave Mechanics. bisacsh Quantum field theory Mathematical models fast |
| title | Non-perturbative methods in 2 dimensional quantum field theory / |
| title_alt | 2 dimensional quantum field theory |
| title_auth | Non-perturbative methods in 2 dimensional quantum field theory / |
| title_exact_search | Non-perturbative methods in 2 dimensional quantum field theory / |
| title_full | Non-perturbative methods in 2 dimensional quantum field theory / Elcio Abdalla, M. Cristina B. Abdalla, Klaus D. Rothe. |
| title_fullStr | Non-perturbative methods in 2 dimensional quantum field theory / Elcio Abdalla, M. Cristina B. Abdalla, Klaus D. Rothe. |
| title_full_unstemmed | Non-perturbative methods in 2 dimensional quantum field theory / Elcio Abdalla, M. Cristina B. Abdalla, Klaus D. Rothe. |
| title_short | Non-perturbative methods in 2 dimensional quantum field theory / |
| title_sort | non perturbative methods in 2 dimensional quantum field theory |
| topic | Quantum field theory Mathematical models. Théorie quantique des champs Modèles mathématiques. SCIENCE Waves & Wave Mechanics. bisacsh Quantum field theory Mathematical models fast |
| topic_facet | Quantum field theory Mathematical models. Théorie quantique des champs Modèles mathématiques. SCIENCE Waves & Wave Mechanics. Quantum field theory Mathematical models |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235841 |
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