Introduction to the functional renormalization group:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2010
|
| Series: | Lecture notes in physics
798 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 375 S. graph. Darst. |
| ISBN: | 9783642050930 9783642050947 |
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Record in the Search Index
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| adam_text | 3.3.1 RG FIXED POINTS AND THE CRITICAL SURFACE 72 CONTENTS PART I
FOUNDATIONS OF THE RENORMALIZATION GROUP 1 PHASE TRANSITIONS AND THE
SCALING HYPOTHESIS 5 1. 1 CLASSIFICATION OF PHASE TRANSITIONS 5 1.2
CRITICAL EXPONENTS AND UNIVERSALITY OF CONTINUOUS PHASE TRANSITIONS 9
1.3 THE SCALING HYPOTHESIS 12 1.4 SCALING IN THE VICINITY OF QUANTUM
CRITICAL POINTS 15 REFERENCES 21 2 MEAN-FIELD THEORY AND THE GAUSSIAN
APPROXIMATION 23 2.1 MEAN-FIELD THEORY 24 2.1.1 LANDAU FUNCTION AND FREE
ENERGY 24 2.1.2 THERMODYNAMIC CRITICAL EXPONENTS 26 2.2 GINZBURG-LANDAU
THEORY 30 2.2.1 EXACT EFFECTIVE FIELD THEORY 30 2.2.2 TRUNCATED
EFFECTIVE ACTION: 4 -THEORY 34 2.3 THE GAUSSIAN APPROXIMATION 39 2.3.1
GAUSSIAN EFFECTIVE ACTION 39 2.3.2 GAUSSIAN CORRECTIONS TO THE SPECIFIC
HEAT EXPONENT 41 2.3.3 CORRELATION FUNCTION 44 2.3.4 FAILURE OF THE
GAUSSIAN APPROXIMATION IN D 4 47 REFERENCES 52 3 WILSONIAN
RENORMALIZATION GROUP 53 3.1 THE BASIC IDEA 54 3.2 REAL-SPACE RG FOR THE
ONE-DIMENSIONAL ISING MODEL 61 3.2.1 EXACT DECIMATION 61 3.2.2 ITERATION
AND FIXED POINTS OF THE RG 66 3.2.3 INFINITESIMAL FORM OF RG RECURSION
RELATIONS 69 3.3 GENERAL PROPERTIES OF RG FLOWS 72 BIBLIOGRAFISCHE
INFORMATIONEN HTTP://D-NB.INFO/997432764 DIGITALISIERT DURCH TII
CONTENTS 3.3.2 LOCAL RG FLOW CLOSE TO A FIXED POINT: CLASSIFICATION OF
COUPLINGS AND JUSTIFICATION OF THE SCALING HYPOTHESIS . 75 3.3.3 GLOBAL
PROPERTIES OF RG FLOWS AND CLASSIFICATION OF FIXED POINTS 81 REFERENCES
87 4 CRITICAL BEHAVIOR OF THE ISING MODEL CLOSE TO FOUR DIMENSIONS 91
4.1 DIAGRAMMATIC PERTURBATION THEORY 91 4.1.1 WICK THEOREM 93 4.1.2
FEYNMAN DIAGRAMS AND LINKED CLUSTER THEOREM 95 4.1.3 DIAGRAMS FOR
CORRELATION FUNCTIONS AND THE IRREDUCIBLE SELF-ENERGY 98 4.2 ONE-LOOP
MOMENTUM SHELL RG 101 4.2.1 DERIVATION OF THE RG FLOW EQUATIONS 102
4.2.2 THE WILSON-FISHER FIXED POINT 108 4.2.3 WAVE FUNCTION
RENORMALIZATION AND ANOMALOUS DIMENSION 113 REFERENCES 120 5
FIELD-THEORETICAL RENORMALIZATION GROUP 123 5.1 DIVERGENCIES AND THEIR
REGULARIZATION IN FIELD THEORY 123 5.2 PERTURBATIVE RENORMALIZATION 128
5.2.1 THE RENORMALIZED LAGRANGIAN 128 5.2.2 PERTURBATIVE CALCULATION OF
RENORMALIZATION FACTORS 130 5.2.3 RELATING RENORMALIZED PERTURBATION
THEORY TO EXPERIMENTS 133 5.3 CALLAN-SYMANZIK EQUATION 135 REFERENCES
139 PART II INTRODUCTION TO THE FUNCTIONAL RENORMALIZATION GROUP 6
FUNCTIONAL METHODS 147 6.1 GENERATING FUNCTIONALS FOR GREEN FUNCTIONS
150 6.1.1 DISCONNECTED GREEN FUNCTIONS 150 6.1.2 CONNECTED GREEN
FUNCTIONS 151 6.1. CONTENTS XIII 7 EXACT FRG FLOW EQUATIONS 181 7.1
CUTOFFS 181 7.2 EXACT FRG FLOW EQUATIONS FOR GENERATING FUNCTIONALS 186
7.2.1 DISCONNECTED GREEN FUNCTIONS 187 7.2.2 CONNECTED GREEN FUNCTIONS
188 7.2.3 AMPUTATED CONNECTED GREEN FUNCTIONS 189 7.2.4 ONE-LINE
IRREDUCIBLE VERTICES 190 7.3 EXACT FRG EQUATIONS FOR THE IRREDUCIBLE
VERTICES 194 7.4 SPONTANEOUS SYMMETRY BREAKING: THE VERTEX EXPANSION
WITH VACUUM EXPECTATION VALUES 200 REFERENCES 207 8 VERTEX EXPANSION 209
8.1 VERTEX EXPANSION FOR CLASSICAL 4 -THEORY 210 8.1.1 EXACTFRGFLOW
EQUATIONS 212 8.1.2 RESCALED FLOW EQUATIONS 213 8.1.3 FRG FLOW EQUATIONS
FOR A SHARP MOMENTUM CUTOFF 217 8.2 RECOVERING THE MOMENTUM SHELL
RESULTS FROM THE FRG 219 8.3 MOMENTUM-DEPENDENT SELF-ENERGY IN THE
SYMMETRIC PHASE 221 8.3.1 SCALING FUNCTIONS 221 8.3.2 TRUNCATION
STRATEGY BASED ON RELEVANCE 222 8.3.3 FRG RESULTS FOR THE SELF-ENERGY
SCALING FUNCTION 228 8.4 MOMENTUM-DEPENDENT SELF-ENERGY IN THE
SYMMETRY-BROKEN PHASE 229 REFERENCES 232 9 DERIVATIVE EXPANSION 233 9.1
DERIVATIVE EXPANSION FOR THE O(A0-SYMMETRIC CLASSICAL /-THEORY 233 9.2
LOCAL POTENTIAL APPROXIMATION 237 9.2.1 RG EQUATION FOR THE EFFECTIVE
POTENTIAL 237 9.2.2 FIXED POINTS AND CRITICAL EXPONENTS 239 9. XIV
CONTENTS 10.3.1 LADDER APPROXIMATION IN THE PARTICLE-PARTICLE CHANNEL ..
269 10.3.2 RANDOM PHASE APPROXIMATION IN THE FORWARD SCATTERING CHANNEL
273 10.4 RESCALED FLOW EQUATIONS AND DEFINITION OF THE FERMI SURFACE
....274 10.4.1 SCALING TOWARD THE FERMI SURFACE 275 10.4.2
CLASSIFICATION OF COUPLINGS 282 10.4.3 EXACT INTEGRAL EQUATION FOR THE
FERMI SURFACE 284 10.5 ONE-LOOP PATCHING APPROXIMATIONS 285 10.5.1 FLOW
OF MARGINAL COUPLINGS 287 10.5.2 SPINLESS FERMIONS 290 10.5.3
ONE-DIMENSIONAL G-OLOGY FOR SI/(2)-INVARIANT MODELS ... 292 10.5.4
MANY-PATCH RG FOR THE SQUARE-LATTICE HUBBARD MODEL .. 297 REFERENCES 302
11 NORMAL FERMIONS: PARTIAL BOSONIZATION IN THE FORWARD SCATTERING
CHANNEL 305 11.1 HUBBARD-STRATONOVICH TRANSFORMATION IN THE FORWARD
SCATTERING CHANNEL 307 11.2 EXACT FRG FLOW EQUATIONS 310 11.3
DYSON-SCHWINGER AND SKELETON EQUATIONS 315 11.4 WARD IDENTITIES 317 11.5
EXACT SOLUTION OF THE FRG FLOW EQUATIONS FOR FERMIONS WITH LINEAR
DISPERSION VIA WARD IDENTITIES 322 REFERENCES 324 12 SUPERFLUID
FERMIONS: PARTIAL BOSONIZATION IN THE PARTICLE-PARTICLE CHANNEL 327 12.1
HUBBARD-STRATONOVICH TRANSFORMATION IN THE PARTICLE-PARTICLE CHANNEL 328
12.2 MEAN-FIELD APPROXIMATION AND BCS-BEC CROSSOVER 330 12.3 GAUSSIAN
FLUCTUATIONS 335 12.3.1 GAUSSIAN EFFECTIVE ACTION 335 12.3.
|
| any_adam_object | 1 |
| author | Kopietz, Peter 1961- Bartosch, Lorenz 1969- Schütz, Florian 1976- |
| author_GND | (DE-588)115248021 (DE-588)122464028 (DE-588)130403296 |
| author_facet | Kopietz, Peter 1961- Bartosch, Lorenz 1969- Schütz, Florian 1976- |
| author_role | aut aut aut |
| author_sort | Kopietz, Peter 1961- |
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| dewey-full | 530.1 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.1 |
| dewey-search | 530.1 |
| dewey-sort | 3530.1 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Book |
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| isbn | 9783642050930 9783642050947 |
| language | English |
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| physical | XIV, 375 S. graph. Darst. |
| publishDate | 2010 |
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| series | Lecture notes in physics |
| series2 | Lecture notes in physics |
| spelling | Kopietz, Peter 1961- Verfasser (DE-588)115248021 aut Introduction to the functional renormalization group P. Kopietz ; L. Bartosch ; F. Schütz Berlin [u.a.] Springer 2010 XIV, 375 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in physics 798 Renormierungsgruppe (DE-588)4177773-6 gnd rswk-swf Renormierungsgruppe (DE-588)4177773-6 s DE-604 Bartosch, Lorenz 1969- Verfasser (DE-588)122464028 aut Schütz, Florian 1976- Verfasser (DE-588)130403296 aut Lecture notes in physics 798 (DE-604)BV000003166 798 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020411277&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kopietz, Peter 1961- Bartosch, Lorenz 1969- Schütz, Florian 1976- Introduction to the functional renormalization group Lecture notes in physics Renormierungsgruppe (DE-588)4177773-6 gnd |
| subject_GND | (DE-588)4177773-6 |
| title | Introduction to the functional renormalization group |
| title_auth | Introduction to the functional renormalization group |
| title_exact_search | Introduction to the functional renormalization group |
| title_full | Introduction to the functional renormalization group P. Kopietz ; L. Bartosch ; F. Schütz |
| title_fullStr | Introduction to the functional renormalization group P. Kopietz ; L. Bartosch ; F. Schütz |
| title_full_unstemmed | Introduction to the functional renormalization group P. Kopietz ; L. Bartosch ; F. Schütz |
| title_short | Introduction to the functional renormalization group |
| title_sort | introduction to the functional renormalization group |
| topic | Renormierungsgruppe (DE-588)4177773-6 gnd |
| topic_facet | Renormierungsgruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020411277&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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