Introduction to the Functional Renormalization Group

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Springer Science & Business Media, 03.05.2010 - 380 Seiten
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This book, based on a graduate course given by the authors, is a pedagogic and self-contained introduction to the renormalization group with special emphasis on the functional renormalization group. The functional renormalization group is a modern formulation of the Wilsonian renormalization group in terms of formally exact functional differential equations for generating functionals.

In Part I the reader is introduced to the basic concepts of the renormalization group idea, requiring only basic knowledge of equilibrium statistical mechanics. More advanced methods, such as diagrammatic perturbation theory, are introduced step by step.

Part II then gives a self-contained introduction to the functional renormalization group. After a careful definition of various types of generating functionals, the renormalization group flow equations for these functionals are derived. This procedure is shown to encompass the traditional method of the mode elimination steps of the Wilsonian renormalization group procedure. Then, approximate solutions of these flow equations using expansions in powers of irreducible vertices or in powers of derivatives are given.

Finally, in Part III the exact hierarchy of functional renormalization group flow equations for the irreducible vertices is used to study various aspects of non-relativistic fermions, including the so-called BCS-BEC crossover, thereby making the link to contemporary research topics.

 

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Inhalt

I
5
II
9
III
12
IV
15
V
21
VI
23
VII
24
VIII
26
LXII
194
LXIII
200
LXIV
207
LXV
209
LXVI
210
LXVII
212
LXVIII
213
LXIX
217

IX
30
XI
34
XII
39
XIV
41
XV
44
XVI
47
XVII
52
XVIII
53
XIX
54
XX
61
XXII
66
XXIII
69
XXIV
72
XXVI
75
XXVII
81
XXVIII
87
XXIX
90
XXX
93
XXXI
95
XXXII
98
XXXIII
101
XXXIV
102
XXXV
108
XXXVI
113
XXXVII
120
XXXVIII
123
XXXIX
128
XL
130
XLI
133
XLII
135
XLIII
139
XLIV
147
XLV
150
XLVI
151
XLVII
156
XLVIII
159
XLIX
160
L
163
LI
167
LII
169
LIII
171
LIV
176
LV
179
LVI
181
LVII
186
LVIII
187
LIX
188
LX
189
LXI
190
LXX
219
LXXI
221
LXXII
222
LXXIII
228
LXXIV
229
LXXV
232
LXXVI
233
LXXVII
237
LXXIX
239
LXXX
242
LXXXI
247
LXXXII
255
LXXXIII
259
LXXXIV
262
LXXXV
268
LXXXVI
269
LXXXVIII
273
LXXXIX
274
XC
275
XCI
282
XCII
284
XCIII
285
XCIV
287
XCV
290
XCVI
292
XCVII
297
XCVIII
302
XCIX
305
C
307
CI
310
CII
315
CIII
317
CIV
322
CV
324
CVI
327
CVII
328
CVIII
330
CIX
335
CXI
339
CXII
342
CXIV
345
CXV
346
CXVI
347
CXVII
351
CXVIII
357
CXIX
362
CXX
365
CXXI
369
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