Novel use of Legendre transformation in field theory and many particle systems: on-shell expansion and inversion method
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Kyoto
Yukawa Inst. for Theoretical Physics u.a.
1995
|
| Series: | [Progress of theoretical physics / Supplement]
121 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 428 S. |
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| 245 | 1 | 0 | |a Novel use of Legendre transformation in field theory and many particle systems |b on-shell expansion and inversion method |c Reijiro Fukuda ... |
| 264 | 1 | |a Kyoto |b Yukawa Inst. for Theoretical Physics u.a. |c 1995 | |
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| adam_text | IMAGE 1
2 R. FUKUDA, M. KOMACHIYA, S. YOKOJIMA, Y. SUZUKI, K. OKUMURA AND T.
INAGAKI
CONTENTS
INTRODUCTION 7
CHAPTER I. ACTION FUNCTIONAL 10
§ 1.1. ACTION FUNCTIONAL IN CLASSICAL MECHANICS § 1.2. EFFECTIVE ACTION
IN QUANTUM FIELD THEORY
CHAPTER II. ON-SHELL EXPANSION OF EFFECTIVE ACTION 18
§ 2.1. BASIC FORMULATION § 2.2. ON-SHELL VARIATION, COHERENT STATE AND
CONNECTED S-MATRIX ELEMENT § 2.3. SOURCE AT THE BOUNDARY T = TI, T F §
2.4. GENERALIZATION TO COMPOSITE FIELD CASE
§ 2.5. GRASSMANN NUMBER CASE 2.5.1. LEGENDRE TRANSFORMATION IN GRASSMANN
NUMBER CHANNEL 2.5.2. ON-SHELL EXPANSION IN GRASSMANN NUMBER CHANNEL
CHAPTER III. APPLICATIONS OF ON-SHELL EQUATION 40
§ 3.1. 1, 2, 3-BODY BETHE-SALPETER EQUATIONS 3.1.1. 1-BODY CHANNEL
3.1.2. 2-BODY CHANNEL 3.1.3. 3-BODY CHANNEL § 3.2. ROLE OF SELF-ENERGY
IN LADDER APPROXIMATION § 3.3. CRITERION FOR STABILITY OF QUANTUM SYSTEM
§ 3.4. ON-SHELL BOUND STATE EQUATION
3.4.1. ON-SHELL BS EQUATION 3.4.2. PERTURBATIVE CALCULATION OF T~ L
3.4.3. EXAMPLES OF XFT THEORY
§ 3.5. SYMMETRY BREAKING AND GOLDSTONE MODE
CHAPTER IV. S-MATRIX AND CONDENSED VACUUM 57
§ 4.1. QCD AND QUARK-LINE PHYSICS § 4.2. TWO-DIMENSIONAL QCD § 4.3.
ON-SHELL VARIATION AND DIFFERENT VACUA 4.3.1. CLASSICAL MECHANICS
4.3.2. FIELD THEORETICAL CASE
CHAPTER V. IV-BODY BOUND STATE EQUATION 74
§ 5.1. IV-BODY BOUND STATE EQUATION BY LEGENDRE TRANSFORMATION
IMAGE 2
CONTENTS
§ 5.2. INTERPRETATION OF CN~N § 5.3. INVERSE OF CN7N
CHAPTER VI. LEGENDRE TRANSFORMATION THROUGH DIAGRAMS.
§ 6.1. SUM-UP RULE FOR GENERAL Z -POINT CONNECTED GREEN S FUNCTIONS
6.1.1. TRANSFORMATION FROM /I TO G 6.1.2. TRANSFORMATION FROM JZ TO GZ
6.1.3. TRANSFORMATION FROM H TO G 3 6.1.4. TRANSFORMATION FROM J* TO GA
6.1.5. DIFFICULTY OF TRANSFORMATION FROM /,- TO GI (I 5) § 6.2.
DERIVATION OF GENERALIZED BOUND STATE EQUATION 6.2.1. 1, 2 AND 3-BODY BS
EQUATIONS
6.2.2. 4-BODY BS EQUATION § 6.3. GRAPHICAL RULE FOR /,*: INVERSION
FORMULA
CHAPTER VII. INVERSION METHOD 104
§ 7.1. BASIC PRINCIPLE § 7.2. INVERSION FORMULA 7.2.1. STATIC CASE
7.2.2. EXCITED STATE BY INVERSION METHOD
- GENELIZATION OF ON-SHELL EQUATION - § 7.3. SOME EXAMPLES 7.3.1.
CONTACT 2-BODY INTERACTION 7.3.2. SCHWINGER-DYSON EQUATION IN THE LADDER
APPROXIMATION
7.3.3. GAUGE INVARIANT STUDY OF STRONG COUPLING PHASE OF MASSLESS QED
7.3.4. ISING MODEL BY INVERSION METHOD § 7.4. IMPROVEMENT BY
RENORMALIZATION GROUP: CASE OF QCD 7.4.1. CALLAN-SYMANZIK EQUATION
7.4.2. SCALE INVARIANT FORMULA
CHAPTER VIII. ATOMIC SYSTEM 127
§ 8.1. MULTI-TIME SCHRODINGER EQUATION 8.1.1. HYDROGEN ATOM 8.1.2.
HELIUM ATOM 8.1.3. LITHIUM ATOM 8.1.4. IV-ELECTRON ATOM 8.1.5.
IV-ELECTRON SYSTEM -ORDINARY SCHRODINGER EQUATION - § 8.2. DENSITY
FUNCTIONAL THEORY BY LEGENDRE TRANSFORMATION
8.2.1. ATOMIC SYSTEM WITH N ELECTRONS 8.2.2. SPIN DENSITY FUNCTIONAL
8.2.3. HOHENBERG-KOHN THEOREM 8.2.4. EXCITATION SPECTRUM
IMAGE 3
4 R. FUKUDA, M. KOMACHIYA, S. YOKOJIMA, Y. SUZUKI, K. OKUMURA AND T.
INAGAKI
8.2.5. METHOD OF AUXILIARY FIELD § 8.3. GENERALIZATION: IONIZATION AND
AFFINITY ENERGY 8.3.1. IONIZATION (AFFINITY) ENERGY
8.3.2. MULTIPLE IONIZATION (AFFINITY) ENERGY AND SCHRODINGER EQUATION
8.3.3. NON-LOCAL DENSITY § 8.4. 5-MATRIX APPROACH OF ATOMIC SCATTERING
BY EFFECTIVE ACTION § 8.5. Z 1 EXPANSION
8.5.1. ENERGY LEVELS 8.5.2. SCATTERING MATRIX ELEMENT
CHAPTER IX. SUPERCONDUCTIVITY BY INVERSION METHOD 158
§ 9.1. APPLICATION TO EQUILIBRIUM SYSTEM 9.1.1. HAMILTONIAN 9.1.2.
THERMODYNAMICS OF SUPERCONDUCTOR
§ 9.2. APPLICATION TO NON-EQUILIBRIUM SYSTEM 9.2.1. HAMILTONIAN 9.2.2.
PERTURBATION SERIES FOR CONTOUR-ORDERED GREEN S FUNCTION 9.2.3.
DERIVATION OF GENERALIZED GORKOV S EQUATION 9.2.4. EFFECT OF DIRECT
COULOMB REPULSION
CHAPTER X. HUBBARD MODEL BY INVERSION METHOD 185
§ 10.1. FERROMAGNETIC PHASE BY WEAK COUPLING EXPANSION 10.1.1.
FERROMAGNETISM BY ZI SYMMETRIC INVERSION UP TO SECOND ORDER 10.1.2.
FIRST ORDER OF INVERSION METHOD - STONER THEORY - 10.1.3. SECOND ORDER
OF INVERSION METHOD - SPIN FLUCTUATION - 10.1.4. SU(2) SYMMETRIC STONER
THEORY 10.1.5. EXCITATION MODES - ON-SHELL EQUATION - 10.1.6. SECOND
DERIVATIVE OF EFFECTIVE ACTION 10.1.7. STUDY OF EXCITATION MODES
§ 10.2. STRONG COUPLING INVERSION 10.2.1. FERROMAGNETIC STATE 10.2.2.
ANTIFERROMAGNETIC STATE 10.2.3. NUMERICAL CALCULATION
CHAPTER XI. HIGHER ORDERS OF INVERSION SERIES 218
§ 11.1. QED AND ${X)4 {X) § 11.2. PERTURBATIVE CONSTRUCTION OF EFFECTIVE
ACTION: PROOF OF THEOREMS § 11.3. APPLICATIONS 11.3.1. MASSLESS QED -
CHANGE OF ORDER PARAMETER -
11.3.2. EXCITED STATES § 11.4. CASE OF QCD
IMAGE 4
CONTENTS 5
§ 11.5. FI 4 MODEL 11.5.1. LOCAL COMPOSITE OPERATOR 11.5.2. NON-LOCAL
COMPOSITE OPERATOR § 11.6. ITINERANT ELECTRON MODEL § 11.7. ISING MODEL
CHAPTER XII. NON-EQUILIBRIUM GENERATING FUNCTIONAL W[JI, J 2 ] AND
F[4 , FA].. 250
§ 12.1. DEFINITION OF W{JU H] AND F[FA, FA] § 12.2. RELATIONS INVOLVING
W[J U J 2 ] AND F[FA, FA] 12.2.1. IDENTITIES OF SECOND DERIVATIVE
12.2.2. EXPANSION OF W OR F IN POWERS OF Z OR J { ~ )
§ 12.3. ON-SHELL EXPANSION OF F[FA, FA]
12.3.1. CASE OF HERMITE FIELD 12.3.2. NON-HERMITE CASE - SUPERFLUID 4 HE
- 12.3.3. RELATION BETWEEN REAL AND IMAGINARY TIME ON-SHELL EXPANSION §
12.4. CLASSICAL AND MACROSCOPIC LIMIT: REPARAMETRIZATION OF / ( ~
12.4.1. CLASSICAL LIMIT OF W[J U J 2 ] 12.4.2. CLASSICAL LIMIT OF F[FA,
FA]
12.4.3. MACROSCOPIC LIMIT § 12.5. MODEL CALCULATION WITH INITIAL
EQUILIBRIUM 12.5.1. THE MODEL 12.5.2. DISSIPATION THROUGH INVERSION
METHOD § 12.6. ADIABATIC INVERSION: TDGL EQUATION
12.6.1. ADIABATIC EXPANSION 12.6.2. EQUILIBRIUM TERM 12.6.3. INVERSION
AND TDGL
CHAPTER XIII. QUANTUM MECHANICS 299
§ 13.1. ENERGY LEVELS BY EFFECTIVE ACTION 13.1.1. ENERGY LEVELS BY
EFFECTIVE ACTION - LOCAL SOURCE - 13.1.2. FAILURE OF LADDER
APPROXIMATION - BILOCAL SOURCE - 13.1.3. FIELD THEORY § 13.2. STATIONARY
PHASE AND LEGENDRE TRANSFORMATION § 13.3. EFFECTIVE ACTION OF FINITE
TIME INTERVAL
13.3.1. EFFECTIVE ACTION OF SINGLE VARIABLE 13.3.2. EFFECTIVE ACTION OF
DOUBLE VARIABLES § 13.4. HILBERT SPACE OF MACROSCOPIC SYSTEM 13.4.1.
WAVE FUNCTION OF IV-PARTICLE SYSTEM
13.4.2. SECOND QUANTIZED SYSTEM 13.4.3. EIGENFUNCTIONAL OF HAMILTONIAN
13.4.4. STRUCTURE OF HILBERT SPACE 13.4.5. TIME EVOLUTION § 13.5.
MESUREMENT THEORY IN TERMS OF MACROVARIABLES
IMAGE 5
R. FUKUDA, M. KOMACHIYA, S. YOKOJIMA, Y. SUZUKI, K. OKUMURA AND T.
INAGAKI
CHAPTER XIV. SUPERFLUID 4 HE 329
§ 14.1. CONDENSATION ^ AND ^ § 14.2. PAIRING IN SUPERFLUID HE §
14.3. WARD-TAKAHASHI IDENTITIES FOR MASS FLOW 14.3.1. DERIVATION OF W-T
IDENTITIES
14.3.2. CONDENSATION AND CORRELATION FUNCTIONS - DEFINITION OF N N AND N
S - § 14.4. SUPERFLUID FLOW 14.4.1. EXISTENCE OF SOLUTION OF SUPERFLOW
14.4.2. W-T IDENTITIES IN PRESENCE OF SUPERFLOW § 14.5. HYDRODYNAMIC
EQUATION OF TWO FLUID MODEL 14.5.1. DERIVATION OF ENERGY-MOMENTUM TENSOR
THROUGH SPACE-TIME TRANSLA- TION INVARIANCE
14.5.2. W-T IDENTITIES INVOLVING ENERGY-MOMENTUM TENSOR 14.5.3. MASS
FLUX 14.5.4. ENERGY-MOMENTUM TENSOR WITH SUPERFLOW 14.5.5. ENERGY AND
ENERGY FLUX 14.5.6. ENTROPY CONSERVATION 14.5.7. INHOMOGENEOUS SUPERFLOW
14.5.8. GALILEAN TRANSFORMATION
APPENDIXES 382
A. FORMULAS OF LEGENDRE TRANSFORMATION B. FEYNMAN PRESCRIPTION AND LARGE
TIME LIMIT OF KERNEL C. DIGRAMMATICAL RULE OF LEGENDRE TRANSFORMATION D.
IN-FIELD OUT-FIELD FORMALISM E. CALCULATION OF WO[J , J2] OF HARMONIC
OSCILLATOR
F. DIGRAMMATICAL RULE OF W[ J , J2] WITH ARBITRARY INITIAL DISTRIBUTION
G. FEYNMAN RULE WITH INITIAL EQUILIBRIUM H. FERMION PATH INTEGRAL AND
FEYNMAN RULE FOR HUBBARD MODEL
I. INVERSION FORMULAS OF MANY VARIABLES J. LOOP EXPANSION OF F AND
PROPAGATORS FOR SUPERFLUID 4 HE
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| indexdate | 2024-07-09T17:59:21Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007225559 |
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| physical | 428 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Yukawa Inst. for Theoretical Physics u.a. |
| record_format | marc |
| series2 | [Progress of theoretical physics / Supplement] |
| spelling | Novel use of Legendre transformation in field theory and many particle systems on-shell expansion and inversion method Reijiro Fukuda ... Kyoto Yukawa Inst. for Theoretical Physics u.a. 1995 428 S. txt rdacontent n rdamedia nc rdacarrier [Progress of theoretical physics / Supplement] 121 Relativistische Quantenfeldtheorie (DE-588)4177686-0 gnd rswk-swf Vielteilchensystem (DE-588)4063491-7 gnd rswk-swf Legendre-Transformation (DE-588)4332841-6 gnd rswk-swf Vielteilchensystem (DE-588)4063491-7 s Legendre-Transformation (DE-588)4332841-6 s DE-604 Relativistische Quantenfeldtheorie (DE-588)4177686-0 s Fukuda, Reijiro Sonstige oth Supplement] [Progress of theoretical physics 121 (DE-604)BV002573679 121 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007225559&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Novel use of Legendre transformation in field theory and many particle systems on-shell expansion and inversion method Relativistische Quantenfeldtheorie (DE-588)4177686-0 gnd Vielteilchensystem (DE-588)4063491-7 gnd Legendre-Transformation (DE-588)4332841-6 gnd |
| subject_GND | (DE-588)4177686-0 (DE-588)4063491-7 (DE-588)4332841-6 |
| title | Novel use of Legendre transformation in field theory and many particle systems on-shell expansion and inversion method |
| title_auth | Novel use of Legendre transformation in field theory and many particle systems on-shell expansion and inversion method |
| title_exact_search | Novel use of Legendre transformation in field theory and many particle systems on-shell expansion and inversion method |
| title_full | Novel use of Legendre transformation in field theory and many particle systems on-shell expansion and inversion method Reijiro Fukuda ... |
| title_fullStr | Novel use of Legendre transformation in field theory and many particle systems on-shell expansion and inversion method Reijiro Fukuda ... |
| title_full_unstemmed | Novel use of Legendre transformation in field theory and many particle systems on-shell expansion and inversion method Reijiro Fukuda ... |
| title_short | Novel use of Legendre transformation in field theory and many particle systems |
| title_sort | novel use of legendre transformation in field theory and many particle systems on shell expansion and inversion method |
| title_sub | on-shell expansion and inversion method |
| topic | Relativistische Quantenfeldtheorie (DE-588)4177686-0 gnd Vielteilchensystem (DE-588)4063491-7 gnd Legendre-Transformation (DE-588)4332841-6 gnd |
| topic_facet | Relativistische Quantenfeldtheorie Vielteilchensystem Legendre-Transformation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007225559&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002573679 |
| work_keys_str_mv | AT fukudareijiro noveluseoflegendretransformationinfieldtheoryandmanyparticlesystemsonshellexpansionandinversionmethod |