Bosonization of interacting fermions in arbitrary dimensions:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1997
|
| Series: | [Lecture notes in physics / M]
48 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 259 S. graph. Darst. |
| ISBN: | 3540627200 |
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MARC
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| 100 | 1 | |a Kopietz, Peter |d 1961- |e Verfasser |0 (DE-588)115248021 |4 aut | |
| 245 | 1 | 0 | |a Bosonization of interacting fermions in arbitrary dimensions |c Peter Kopietz |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1997 | |
| 300 | |a XII, 259 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a [Lecture notes in physics / M] |v 48 | |
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CONTENTS
PART
I.
DEVELOPMENT
OF
THE
FORMALISM
1.
INTRODUCTION
.
3
1.1
PERTURBATION
THEORY
AND
QUASI-PARTICLES
.
3
1.2
A
BRIEF
HISTORY
OF
BOSONIZATION
IN
D
1
.
5
1.3
THE
SCOPE
OF
THIS
BOOK
.
8
1.4
NOTATIONS
AND
ASSUMPTIONS
.
9
2.
FERMIONS
AND
THE
FERMI
SURFACE
.
11
2.1
THE
GENERIC
MANY-BODY
HAMILTONIAN
.
11
2.2
THE
SINGLE-PARTICLE
GREEN
'
S
FUNCTION
.
14
2.2.1
DEFINITION
OF
THE
GREEN
'
S
FUNCTION
.
14
2.2.2
DEFINITION
OF
THE
INTERACTING
FERMI
SURFACE
.
.
15
2.2.3
LANDAU
FERMI
LIQUIDS
.
16
2.3
THE
DENSITY-DENSITY
CORRELATION
FUNCTION
.
20
2.4
PATCHING
THE
FERMI
SURFACE
.
22
2.4.1
DEFINITION
OF
THE
PATCHES
AND
BOXES
.
22
2.4.2
LINEARIZATION
OF
THE
ENERGY
DISPERSION
.
25
2.4.3
AROUND-THE-CORNER
PROCESSES
AND
THE
PROPER
CHOICE
OF
THE
CUTOFFS
.
27
2.5
CURVED
PATCHES
AND
REDUCTION
OF
THE
PATCH
NUMBER
.
28
2.6
SUMMARY
AND
OUTLOOK
.
31
3.
HUBBARD-STRATONOVICH
TRANSFORMATIONS
.
33
3.1
GRASSMANNIAN
FUNCTIONAL
INTEGRALS
.
33
3.2
THE
FIRST
HUBBARD-STRATONOVICH
TRANSFORMATION
.
36
3.2.1
DECOUPLING
OF
THE
INTERACTION
.
36
3.2.2
TRANSFORMATION
OF
THE
SINGLE-PARTICLE
GREEN
'
S
FUNCTION
.
37
3.3
THE
SECOND
HUBBARD-STRATONOVICH
TRANSFORMATION
.
40
3.3.1
TRANSFORMATION
OF
THE
DENSITY-DENSITY
CORRELATION
FUNCTION
.
40
3.3.2
DEFINITION
OF
THE
BOSONIZED
KINETIC
ENERGY
.
43
3.4
SUMMARY
AND
OUTLOOK
.
43
X
CONTENTS
4.
BOSONIZATION
OF
THE
HAMILTONIAN
AND
THE
DENSITY-DENSITY
CORRELATION
FUNCTION
.
45
4.1
THE
GENERALIZED
CLOSED
LOOP
THEOREM
.
46
4.2
THE
GAUSSIAN
APPROXIMATION
.
51
4.2.1
THE
EFFECTIVE
ACTION
FOR
THE
0
"-FIELD
.
51
4.2.2
THE
GAUSSIAN
PROPAGATOR
OF
THE
0
"
-FIELD
.
53
4.2.3
THE
EFFECTIVE
ACTION
FOR
THE
P
"
-FIELD
.
54
4.2.4
THE
GAUSSIAN
PROPAGATOR
OF
THE
P
A
-FIELD
.
55
4.2.5
THE
BOSONIZED
HAMILTONIAN
.
56
4.3
BEYOND
THE
GAUSSIAN
APPROXIMATION
.
58
4.3.1
GENERAL
EXPANSION
OF
THE
BOSONIZED
KINETIC
ENERGY
.
58
4.3.2
THE
LEADING
CORRECTION
TO
THE
EFFECTIVE
ACTION
.
61
4.3.3
THE
LEADING
CORRECTION
TO
THE
BOSONIC
PROPAGATOR
.
63
4.3.4
THE
HIDDEN
SMALL
PARAMETER
.
65
4.3.5
CALCULATING
CORRECTIONS
TO
THE
RPA
VIA
BOSONIZATION
.
69
4.4
SUMMARY
AND
OUTLOOK
.
71
5.
THE
SINGLE-PARTICLE
GREEN
'
S
FUNCTION
.
73
5.1
THE
GAUSSIAN
APPROXIMATION
WITH
LINEARIZED
ENERGY
DISPERSION
73
5.1.1
THE
GREEN
'
S
FUNCTION
FOR
FIXED
BACKGROUND
FIELD
.
74
5.1.2
GAUSSIAN
AVERAGING:
CALCULATION
OF
THE
DEBYE-WALLER
.
80
5.1.3
THE
GREEN
'
S
FUNCTION
IN
REAL
SPACE
.
82
5.1.4
THE
UNDERLYING
ASYMPTOTIC
WARD
IDENTITY
.
83
5.1.5
THE
FERMI
LIQUID
RENORMALIZATION
FACTORS
Z
A
AND
.
88
5.2
BEYOND
THE
GAUSSIAN
APPROXIMATION
.
92
5.2.1
THE
GREEN
'
S
FUNCTION
FOR
FIXED
BACKGROUND
FIELD
.
94
5.2.2
NON-GAUSSIAN
AVERAGING
.
100
5.3
THE
GAUSSIAN
APPROXIMATION
WITH
NON-LINEAR
ENERGY
DISPERSION
105
5.3.1
THE
AVERAGE
EIKONAL
.
105
5.3.2
THE
PREFACTOR
GREEN
'
S
FUNCTIONS
.
106
5.3.3
CONNECTION
WITH
LOWEST
ORDER
PERTURBATION
THEORY
.
110
5.4
SUMMARY
AND
OUTLOOK
.
114
PART
II.
APPLICATIONS
TO
PHYSICAL
SYSTEMS
6.
SINGULAR
INTERACTIONS
(FQ
~
|
Q
|
-
**)
.
121
6.1
MANIPULATIONS
WITH
THE
HELP
OF
THE
DYNAMIC
STRUCTURE
FACTOR
.
122
6.1.1
NON-LINEAR
ENERGY
DISPERSION
.
122
6.1.2
THE
LIMIT
OF
LINEAR
ENERGY
DISPERSION
.
123
6.1.3
FINITE
VERSUS
INFINITE
PATCH
NUMBER
.
125
6.2
THE
STATIC
DEBYE-WALLER
FACTOR
FOR
LINEARIZED
ENERGY
DISPERSION
127
6.2.1
CONSEQUENCES
OF SPHERICAL
SYMMETRY
.
127
6.2.2
THE
EXISTENCE
OF
THE
QUASI-PARTICLE
RESIDUE
.
131
6.2.3
WHY
THE
COULOMB
INTERACTION
IS
SO
NICE
.
132
CONTENTS
XI
6.2.4
THE
SUB-LEADING
CORRECTIONS
FOR
0
17
2(D
-
1)
.
133
6.2.5
THE
REGIME
77
2(D
-
1)
.
135
6.3
LUTTINGER
LIQUID
BEHAVIOR
IN
D
=
1
.
137
6.4
SUMMARY
AND
OUTLOOK
.
141
7.
QUASI-ONE-DIMENSIONAL
METALS
.
143
7.1
THE
COULOMB
INTERACTION
IN
CHAINS
WITHOUT
INTERCHAIN
HOPPING
144
7.2
FINITE
INTERCHAIN
HOPPING
.
149
7.2.1
THE
4-PATCH
MODEL
.
150
7.2.2
HOW
CURVATURE
KILLS
THE
NESTING
SINGULARITY
.
158
7.2.3
ANOMALOUS
SCALING
IN
A
FERMI
LIQUID
.
160
7.2.4
THE
NESTING
SINGULARITY
FOR
GENERAL
FERMI
SURFACES
.
161
7.3
SUMMARY
AND
OUTLOOK
.
163
8.
ELECTRON-PHONON
INTERACTIONS
.
165
8.1
THE
EFFECTIVE
INTERACTION
.
166
8.1.1
THE
DEBYE
MODEL
.
166
8.1.2
INTEGRATION
OVER
THE
PHONONS
.
169
8.2
THE
DEBYE-WALLER
FACTOR
.
171
8.3
PHONON
ENERGY
SHIFT
AND
PHONON
DAMPING
.
172
8.4
THE
QUASI-PARTICLE
RESIDUE
.
175
8.4.1
ISOTROPIC
PHONON
DISPERSION
.
176
8.4.2
QUASI-ONE-DIMENSIONAL
ELECTRONS
OR
PHONONS
.
177
8.5
SUMMARY
AND
OUTLOOK
.
179
9.
FERMIONS
IN
A
STOCHASTIC
MEDIUM
.
181
9.1
THE
AVERAGE
GREEN
'
S
FUNCTION
.
182
9.1.1
NON-INTERACTING
DISORDERED
FERMIONS
.
182
9.1.2
INTERACTING
DISORDERED
FERMIONS
.
185
9.2
STATIC
DISORDER
.
187
9.3
DYNAMIC
DISORDER
.
189
9.3.1
GAUSSIAN
WHITE
NOISE
.
190
9.3.2
FINITE
CORRELATION
TIME
.
193
9.4
SUMMARY
AND
OUTLOOK
.
194
10.
TRANSVERSE
GAUGE
FIELDS
.
197
10.1
EFFECTIVE
ACTIONS
.
200
10.1.1
THE
COUPLED
MATTER
GAUGE
FIELD
ACTION
.
200
10.1.2
THE
EFFECTIVE
MATTER
ACTION
.
203
10.1.3
THE
EFFECTIVE
GAUGE
FIELD
ACTION
.
205
10.2
THE
GREEN
'
S
FUNCTION
IN
GAUSSIAN
APPROXIMATION
.
207
10.2.1
THE
GREEN
'
S
FUNCTION
FOR
FIXED
GAUGE
FIELD
.
208
10.2.2
GAUSSIAN
AVERAGING
.
209
10.3
TRANSVERSE
SCREENING
.
213
10.3.1
THE
TRANSVERSE
DIELECTRIC
TENSOR
.
213
XII
CONTENTS
10.3.2
SCREENING
AND
GAUGE
INVARIANCE
.
214
10.3.3
THE
TRANSVERSE
DIELECTRIC
FUNCTION
FOR
SPHERICAL
FERMI
SURFACES
.
216
10.4
THE
TRANSVERSE
DEBYE-WALLER
FACTOR
.
218
10.4.1
EXACT
RESCALINGS
.
218
10.4.2
THE
RELEVANCE
OF
CURVATURE
.
221
10.4.3
TWO-DIMENSIONAL
MAXWELL-CHERN-SIMONS
THEORY
.
224
10.5
SUMMARY
AND
OUTLOOK
.
231
APPENDIX:
SCREENING
AND
COLLECTIVE
MODES
.
235
A.L
THE
NON-INTERACTING
POLARIZATION
FOR
SPHERICAL
FERMI
SURFACES
.
235
A.2
THE
DYNAMIC
STRUCTURE
FACTOR
FOR
SPHERICAL
FERMI
SURFACES
.
237
A.3
COLLECTIVE
MODES
FOR
SINGULAR
INTERACTIONS
.
240
A.3.1
THE
COULOMB
INTERACTION
IN
1
D
3
.
240
A.3.2
GENERAL
SINGULAR
INTERACTIONS
.
242
A.4
COLLECTIVE
MODES
FOR
FINITE
PATCH
NUMBER
.
243
REFERENCES
.
247
INDEX
.
256 |
| any_adam_object | 1 |
| author | Kopietz, Peter 1961- |
| author_GND | (DE-588)115248021 |
| author_facet | Kopietz, Peter 1961- |
| author_role | aut |
| author_sort | Kopietz, Peter 1961- |
| author_variant | p k pk |
| building | Verbundindex |
| bvnumber | BV011241257 |
| classification_rvk | UD 8221 UL 4000 |
| classification_tum | PHY 026f |
| ctrlnum | (OCoLC)246856540 (DE-599)BVBBV011241257 |
| discipline | Physik |
| format | Book |
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| id | DE-604.BV011241257 |
| illustrated | Illustrated |
| indexdate | 2024-08-16T00:24:56Z |
| institution | BVB |
| isbn | 3540627200 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007544877 |
| oclc_num | 246856540 |
| open_access_boolean | |
| owner | DE-703 DE-384 DE-19 DE-BY-UBM DE-29T DE-91G DE-BY-TUM DE-11 |
| owner_facet | DE-703 DE-384 DE-19 DE-BY-UBM DE-29T DE-91G DE-BY-TUM DE-11 |
| physical | XII, 259 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Springer |
| record_format | marc |
| series2 | [Lecture notes in physics / M] |
| spelling | Kopietz, Peter 1961- Verfasser (DE-588)115248021 aut Bosonization of interacting fermions in arbitrary dimensions Peter Kopietz Berlin [u.a.] Springer 1997 XII, 259 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier [Lecture notes in physics / M] 48 Wechselwirkung (DE-588)4064937-4 gnd rswk-swf Vielteilchentheorie (DE-588)4331960-9 gnd rswk-swf Elementarteilchenphysik (DE-588)4014414-8 gnd rswk-swf Boson (DE-588)4146396-1 gnd rswk-swf Fermionensystem (DE-588)4252865-3 gnd rswk-swf Fermionensystem (DE-588)4252865-3 s Vielteilchentheorie (DE-588)4331960-9 s Boson (DE-588)4146396-1 s DE-604 Elementarteilchenphysik (DE-588)4014414-8 s 1\p DE-604 Wechselwirkung (DE-588)4064937-4 s 2\p DE-604 M] [Lecture notes in physics 48 (DE-604)BV021852221 48 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007544877&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kopietz, Peter 1961- Bosonization of interacting fermions in arbitrary dimensions Wechselwirkung (DE-588)4064937-4 gnd Vielteilchentheorie (DE-588)4331960-9 gnd Elementarteilchenphysik (DE-588)4014414-8 gnd Boson (DE-588)4146396-1 gnd Fermionensystem (DE-588)4252865-3 gnd |
| subject_GND | (DE-588)4064937-4 (DE-588)4331960-9 (DE-588)4014414-8 (DE-588)4146396-1 (DE-588)4252865-3 |
| title | Bosonization of interacting fermions in arbitrary dimensions |
| title_auth | Bosonization of interacting fermions in arbitrary dimensions |
| title_exact_search | Bosonization of interacting fermions in arbitrary dimensions |
| title_full | Bosonization of interacting fermions in arbitrary dimensions Peter Kopietz |
| title_fullStr | Bosonization of interacting fermions in arbitrary dimensions Peter Kopietz |
| title_full_unstemmed | Bosonization of interacting fermions in arbitrary dimensions Peter Kopietz |
| title_short | Bosonization of interacting fermions in arbitrary dimensions |
| title_sort | bosonization of interacting fermions in arbitrary dimensions |
| topic | Wechselwirkung (DE-588)4064937-4 gnd Vielteilchentheorie (DE-588)4331960-9 gnd Elementarteilchenphysik (DE-588)4014414-8 gnd Boson (DE-588)4146396-1 gnd Fermionensystem (DE-588)4252865-3 gnd |
| topic_facet | Wechselwirkung Vielteilchentheorie Elementarteilchenphysik Boson Fermionensystem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007544877&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV021852221 |
| work_keys_str_mv | AT kopietzpeter bosonizationofinteractingfermionsinarbitrarydimensions |