Verfügbarkeit: Quantum field theory

Quantum field theory: a modern perspective

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Bibliographische Detailangaben
1. Verfasser:	Nair, V. P. (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	New York, NY Springer 2005
Schriftenreihe:	Graduate texts in contemporary physics
Schlagworte:	Champs, Théorie quantique des Quantum field theory Quantenfeldtheorie
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	XIV, 557 S. graph. Darst.
ISBN:	0387213864

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Datensatz im Suchindex

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adam_text	Contents 1 Results in Relativistic Quantum Mechanics ............... 1 1.1 Conventions........................................... 1 1.2 Spin-zero particle ....................................... 1 1.3 Dirac equation ......................................... З 2 The Construction of Fields ............................... 7 2.1 The correspondence of particles and fields ................. 7 2.2 Spin-zero bosons ....................................... 8 2.3 Lagrangian and Hamiltonian ............................. 11 2.4 Functional derivatives ................................... 13 2.5 The field operator for fermions ........................... 14 3 Canonical Quantization ................................... 17 3.1 Lagrangian, phase space, and Poisson brackets ............. 17 3.2 Rules of quantization ................................... 23 3.3 Quantization of a free scalar field ......................... 25 3.4 Quantization of the Dirac field ........................... 28 3.5 Symmetries and conservation laws ........................ 32 3.6 The energy-momentum tensor ............................ 34 3.7 The electromagnetic field ................................ 36 3.8 Energy-momentum and general relativity .................. 37 3.9 Light-cone quantization of a scalar field ................... 38 3.10 Conformai invariance of Maxwell equations ................ 39 4 Commutators and Propagators ........................... 43 4.1 Scalar field propagators ................................. 43 4.2 Propagator for fermions ................................. 50 4.3 Grassman variables and fermions ......................... 51 5 Interactions and the S-matrix ............................ 55 5.1 A general formula for the S-matrix ....................... 55 5.2 Wick s theorem ........................................ 61 5.3 Perturbative expansion of the S-matrix ................... 62 5.4 Decay rates and cross sections ............................ 67 5.5 Generalization to other fields ............................. 69 X Contents 5.6 Operator formula for the iV-point functions ................ 72 6 The Electromagnetic Field ................................ 77 6.1 Quantization and photons ............................... 77 6.2 Interaction with charged particles ........................ 81 6.3 Quantum electrodynamics (QED) ........................ 83 7 Examples of Scattering Processes ......................... 85 7.1 Photon-scalar charged particle scattering .................. 85 7.2 Electron scattering in an external Coulomb field ............ 87 7.3 Slow neutron scattering from a medium ................... 89 7.4 Compton scattering ..................................... 92 7.5 Decay of the тг° meson .................................. 95 7.6 Čerenkov radiation ..................................... 97 7.7 Decay of the p-meson ................................... 99 8 Functional Integral Representations ......................103 8.1 Functional integration for bosonic fields ...................103 8.2 Green s functions as functional integrals ...................105 8.3 Fermionic functional integral .............................108 8.4 The S-matrix functional ................................. Ill 8.5 Euclidean integral and QED .............................112 8.6 Nonlinear sigma models .................................114 8.7 The connected Green s functions .........................119 8.8 The quantum effective action ............................122 8.9 The S-matrix in terms of Γ ..............................126 8.10 The loop expansion .....................................127 9 Renormalization ..........................................133 9.1 The general procedure of renormalization ..................133 9.2 One-loop renormalization ................................135 9.3 The renormalized effective potential ......................144 9.4 Power-counting rules ....................................145 9.5 One-loop renormalization of QED ........................147 9.6 Renormalization to higher orders .........................157 9.7 Counterterms and renormalizability .......................162 9.8 RG equation for the scalar field ..........................169 9.9 Solution to the RG equation and critical behavior ..........173 10 Gauge Theories ...........................................179 10.1 The gauge principle .....................................179 10.2 Parallel transport ......................................183 10.3 Charges and gauge transformations .......................185 10.4 Functional quantization of gauge theories ..................188 10.5 Examples ..............................................194 Contents XI 10.6 BRST symmetry and physical states ......................195 10.7 Ward-Takahashi identities for Q-symmetry ................200 10.8 Renormalization of nonabelian theories ....................203 10.9 The fermionic action and QED again .....................206 10.10 The propagator and the effective charge ..................206 11 Symmetry ................................................219 11.1 Realizations of symmetry ................................ 219 11.2 Ward-Takahashi identities ............................... 221 11.3 Ward-Takahashi identities for electrodynamics ............. 223 11.4 Discrete symmetries .................................... 226 11.5 Low-energy theorem for Compton scattering ............... 232 12 Spontaneous symmetry breaking ..........................237 12.1 Continuous global symmetry .............................237 12.2 Orthogonality of different ground states ...................242 12.3 Goidstone s theorem ....................................244 12.4 Coset manifolds ........................................247 12.5 Nonlinear sigma models .................................249 12.6 The dynamics of Goldstone bosons .......................249 12.7 Summary of results .....................................253 12.8 Spin waves ............................................254 12.9 Chiral symmetry breaking in QCD .......................255 12.10 The effective action ....................................258 12.11 Effective Lagrangians, unitarity of the S-matrix ...........263 12.12 Gauge symmetry and the Higgs mechanism ...............266 12.13 The standard model ....................................270 13 Anomalies I ..............................................281 13.1 Introduction ...........................................281 13.2 Computation of anomalies ...............................282 13.3 Anomaly structure: why it cannot be removed ..............289 13.4 Anomalies in the standard model .........................290 13.5 The Lagrangian for π° decay .............................294 13.6 The axial (7(1) problem .................................295 14 Elements of differential geometry .........................299 14.1 Manifolds, vector fields, and forms ........................299 14.2 Geometrical structures on manifolds and gravity ............310 14.2.1 Riemannian structures and gravity .................310 14.2.2 Complex manifolds ...............................313 14.3 Cohomology groups .....................................315 14.4 Homotopy .............................................319 14.5 Gauge fields ...........................................324 14.5.1 Electrodynamics .................................324 XII Contents 14.5.2 The Dirac monopole: A first look ...................326 14.5.3 Nonabelian gauge fields ...........................327 14.6 Fiber bundles ..........................................329 14.7 Applications of the idea of fiber bundles ...................333 14.7.1 Scalar fields around a magnetic monopole ...........333 14.7.2 Gribov ambiguity ................................334 14.8 Characteristic classes ...................................336 15 Path Integrals ............................................341 15.1 The evolution kernel as a path integral ....................341 15.2 The Schrödinger equation ...............................344 15.3 Generalization to fields ..................................345 15.4 Interpretation of the path integral ........................350 15.5 Nontrivial fundamental group for С .......................351 15.6 The case of П2(С) φ Q ..................................353 16 Gauge theory: configuration space ........................359 16.1 The configuration space .................................359 16.2 The path integral in QCD ...............................364 16.3 Instantons .............................................366 16.4 Fermions and index theorem .............................369 16.5 Baryon number violation in the standard model ............373 17 Anomalies II .............................................377 17.1 Anomalies and the functional integral .....................377 17.2 Anomalies and the index theorem ........................379 17.3 The mixed anomaly in the standard model ................383 17.4 Effective action for flavor anomalies of QCD ...............384 17.5 The global or nonperturbative anomaly ...................386 17.6 The Wess-Zumino- Witten (WZW) action ..................390 17.7 The Dirac determinant in two dimensions .................392 18 Finite temperature and density ...........................399 18.1 Density matrix and ensemble averages ....................399 18.2 Scalar field theory ......................................402 18.3 Fermions at finite temperature and density ................404 18.4 A condition on thermal averages ..........................405 18.5 Radiation from a heated source ..........................406 18.6 Screening of gauge fields: Abelian case ....................409 18.7 Screening of gauge fields: Nonabelian case .................415 18.8 Retarded and time-ordered functions ......................419 18.9 Physical significance of Im Яд .......................... 422 18.10 Nonequilibrium phenomena .............................424 18.11 The imaginary time formalism ...........................430 18.12 Symmetry restoration at high temperatures ...............435 Contents XIII 18.13 Symmetry restoration in the standard model ..............439 19 Gauge theory: Nonperturbative questions ................445 19.1 Confinement and dual superconductivity ..................445 19.1.1 The general picture of confinement .................445 19.1.2 The area law for the Wilson loop ...................447 19.1.3 Topological vortices ...............................449 19.1.4 The nonabelian dual superconductivity ..............454 19.2 t Hooft-Polyakov magnetic monopoles ....................457 19.3 The l/iV-expansion .....................................462 19.4 Mesons and baryons in the /N expansion .................465 19.4.1 Chiral symmetry breaking and mesons ..............466 19.4.2 Baryons .........................................468 19.4.3 Baryon number of the skyrmion ....................470 19.4.4 Spin and flavor for skyrmions ......................472 19.5 Lattice gauge theory ....................................475 19.5.1 The reason for a lattice formulation .................475 19.5.2 Plaquettes and the Wilson action ...................476 19.5.3 The fermion doubling problem .....................479 20 Elements of Geometric Quantization ......................485 20.1 General structures ......................................485 20.2 Classical dynamics ......................................491 20.3 Geometric quantization .................................492 20.4 Topological features of quantization .......................496 20.5 A brief summary of quantization .........................499 20.6 Examples ..............................................500 20.6.1 Coherent states ..................................500 20.6.2 Quantizing the two-sphere .........................501 20.6.3 Compact Kahler spaces of the G/ Я -type ............ 506 20.6.4 Charged particle in a monopole field ................508 20.6.5 Anyons or particles of fractional spin ................510 20.6.6 Field quantization, equal-time, and light-cone ........513 20.6.7 The Chern-Simons theory in 2+1 dimensions ........515 20.6.8 Θ- vacua in a nonabelian gauge theory ...............522 20.6.9 Current algebra for the Wess-Zumino- Witten (WZW) model ...........................................525 AppendixtRelativistic Invariance ..........................533 A-I Poincaré algebra .......................................533 A-2 Unitary representations of the Poincaré algebra ............537 A-3 Massive particles .......................................538 A-4 Wave functions for spin-zero particles .....................540 A-5 Wave functions for spin-! particles .......................542 A-6 Spin-l particles ........................................543 XIV Contents A-7 Massless particles....................................... 544 A-8 Position operators ......................................545 A-9 Isometries, anyons......................................545 Generad References ...........................................549 Index .........................................................551
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spelling	Nair, V. P. Verfasser (DE-588)130082708 aut Quantum field theory a modern perspective V. Parameswaran Nair New York, NY Springer 2005 XIV, 557 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in contemporary physics Champs, Théorie quantique des Quantum field theory Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Quantenfeldtheorie (DE-588)4047984-5 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013097999&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Nair, V. P. Quantum field theory a modern perspective Champs, Théorie quantique des Quantum field theory Quantenfeldtheorie (DE-588)4047984-5 gnd
subject_GND	(DE-588)4047984-5
title	Quantum field theory a modern perspective
title_auth	Quantum field theory a modern perspective
title_exact_search	Quantum field theory a modern perspective
title_full	Quantum field theory a modern perspective V. Parameswaran Nair
title_fullStr	Quantum field theory a modern perspective V. Parameswaran Nair
title_full_unstemmed	Quantum field theory a modern perspective V. Parameswaran Nair
title_short	Quantum field theory
title_sort	quantum field theory a modern perspective
title_sub	a modern perspective
topic	Champs, Théorie quantique des Quantum field theory Quantenfeldtheorie (DE-588)4047984-5 gnd
topic_facet	Champs, Théorie quantique des Quantum field theory Quantenfeldtheorie
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