Lecture notes on field theory in condensed matter physics:
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| 100 | 1 | |a Mudry, Christopher |d 1975- |e Verfasser |0 (DE-588)1051266327 |4 aut | |
| 245 | 1 | 0 | |a Lecture notes on field theory in condensed matter physics |c Christopher Mudry (Paul Scherrer Institut, Switzerland) |
| 264 | 1 | |a New Jersey |b World Scientific |c [2014] | |
| 300 | |a xx, 724 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Festkörper |0 (DE-588)4016918-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Quantenfeldtheorie |0 (DE-588)4047984-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kondensierte Materie |0 (DE-588)4132810-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Feldtheorie |0 (DE-588)4016698-3 |2 gnd |9 rswk-swf |
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| 689 | 0 | 0 | |a Kondensierte Materie |0 (DE-588)4132810-3 |D s |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface
vu
A cknovj ledgments
xi
Bosons
]
j.
The h arm on.
ic
crystal
3
1.1
J n
trod
u C:
ion
3
1.2
Classical
o.n e-
dimensi·
о
n
al
crystal
. ...
З
і
2.1
Discrete
limit
3
1 2.2
Therm
o d y
π
arm
c i.irrut
. . . 6
1.3
Quajntura one-el rmensional crystal
, ... 10
1.3 1 Remunscences
about the harmonic oscillator
... ... 10
1.3 2
Discrete I j jr.
j t
■ . . ............... 14
1.33
ТЪ
er
лао
dynamic iim.it
. . . ... 16
1.4
Higher-
dimensional generaliza
ti ona
....... . . . 17
1.5
Problems
..,.,.... .... .... . . 18
1.
5.1
Absence of crystaJli.ne order in one
алеї
two
dimensions
. 18
2
Bogoìiuoov
theory of a dilute
Bose
gas
25
2.1
Introduction
................... .25
2.2
Second quantisation for bosons
- .... 26
2.3
Bose-Kuistem
cono
ens
ti ti
ο π
and spontaneous symmetry
bxea.kj.cg
.... .... 30
2.4
Di.ute
.Возе
gas Operator
torma.1.;
srn
at vanishing
temo
er
a!; urc
3?
2.4..1
Operator
¡:о.гша.!.ізш.
................... 37
2.4.2
Landajj criterion, .tor superftuiclity
. . .... 42
2.0
Dilute
Bose
gas: Pat.b.- .nteg.;:al
lo mia!
і
s ni
at any cernperature
. . 43
2-5.1
Non-iafceracïiiig
ίΐ ΌΛ λ
=- 0.............. 45
2.5 2
Branci
orn-phase
ap proxima
t j
on
.......... . . 48
X.:
ι
Lecture,
notes
on
fiaid
theory
гп
condensed matter -physics
2.5.3
Beyond the random-phase approximation
.......... 54
2 6
Problems
................................ 57
2.6.1
Magnons
in quantum ferromagnets and antiferrom
agnets
as emergent bosons
...................... 57
Non
Linear Sigma Models
67
3.1
Introduction
............................... 67
3.2
Non
Linear Sigma Models (NLa
M
)................. 68
3.2.1
Definition of
Ο
(TV) NLaM
.................. 68
3.2.2
O(N) NLoM as afield theory on a Riemannian manifold
. 71
3.2.3
O(N) NLctM as a held theory on a symmetric space
... 76
3.2.4
Other examples of NLaM
................... 81
3.3
Fixed point theories, engineering and scaling dimensions,
irrelevant, marginal, axid relevant interactions
............ 81
3.3.1
Fixed-point theories
...................... 84
3.3.2
Two-dimensional
0(2)
NL-oM in the spin wave approxima
tion
............................... 8
Y
3.4
Genera,! method of renorrnalization
................. 93
3.5
PerLurbative expansion of the two point correlation function, up to
one loop for the two-dimensional O{N) Mho
M
........... 94
3 6
Ceti
lan-Sy
manzi.
к
equation obeyed by the spin-spin correlator for
the two-dimensional O(N) NLoM with
N > 2......-..... 103
3.6.1
Non-
ρ
er
turbative
definitions of the
r
enorm
ali.
zed coupling
constant and the wave function reriormahzation
....... 105
3.6.2
Expansion of the renormalized coupling constant, the wave-
function renorrnalization, and the renormalized spin-spin
correlator up to order c/g
....................1.05
3.6.3
Expansion of the bare coupling constant, the wave--function
renormalization, and the renormalized spin-spin correlator
up to order
gţ{
......................... 106
3.6.4
Callan-Symanzik equation obeyed by the spin-spin correlator!
08
3.6.5
Physical interpretation of the Callan-Symanzik equation
. 109
3.6.6
Physical interpretation of the beta function
......... 112
3.7
Beta function for the d-dimensional O(N) NLctM with
d
> 2
and
TV
> 2....................... ..... 114
3.8
Problems
. . ................. 123
3.8.1
The Merrnin Wagner theorem for quantum spin
II
armi
torn
ans.......................... 123
3.8.2
Quantum spin coherent states and the
0(3)
QNLaM
. . 128
3.8.3
Classical O(N) NLoM with TV
> 2:
One-loop RG using
the Berezinskii -Blank
parametrizaţi
on of spin waves
.... 142
3.8.4
O(./V) QNLaM: Large-TV expansion
............. 146
CJonients
xv
3.8.5
O(N) QNLaM
with
N > 2:
One-loop RG using the
Be.rezmskii-Bla.n.k pararnelrizalion
of spin waves
...... 159
4.
Kosterlitz-Thouless transition
163
4.1
Introduction
.............................. 163
4.2
Classical, two-dimensional XY model
................. 163
4.3
The Coulomb gas representation of the classical two-dimensional
XY mode).
. ........................ 174
4.4
Equivalence between the Coulomb gas and Sine-
Gord
on model
. . 175
4.4.1
Definitions and statement of results
............ 175
4.4.2
Formal expansion in powers of the reduced magnetic field
177
4.4.3
Sine-Gordon representation of the spin-spin correlation
function, in the two-dimensional XY model
........ 179
4.4.4
Stability analysis of the
hne
of fixed points in the two-
dimensional Sine-Gordon model
............. 182
4.5
Fugacity
expansion of n-point functions in the Sine-Gordon model
184
4.5.1
Fugacity
expansion of the two-point function
........ 185
4.5.2
Two-point function to lowest order in
h j
lì........
1.86
4-5-3
Two-point function to second order in hj ll
. . , 186
4.6
Koster
li
tz renormalization-group equations
............ 190
4.6.1
Kosterhtz RG equations in the vicinity of X
=
Y
= 0 . . 190
4.6.2
Correlation length near X
-=
Y
= 0........... 194
4.6.3
Universal jump of the spin stiffness
............. 198
4.7
Problems
............ ............. 199
4.7.1
The classical two-dimensional random phase XY model
. . 199
Fermions
207
5.
Non-
interact
mg
fermions
209
5.1
Introduction
............................... 209
5.2
Second quantization for
fermions
................... 210
5.3
The non-interacting jeLLium model
.... ... 214
5.31
Thermodynamics without magnetic field
....... 215
5.3.2 Sommerfeld
semi classical theory
Öltransport...... 223
5.3.3 Pauli paramagnetism .... . . . . 228
5-3.4
Landau levels in a magnetic field.
..... . 230
5.4
Time ordered Green functions
................. 233
5.4.1
Definitions
................ ..... 233
5.4.2
Time-ordered Green functions in imaginary tune
.... 235
5 4-3
Time-ordered Green functions in real time
......... 240
5.4.4
Application
to
Lhe
non-interacting jellium model
.... 241
χν.ι
Lecture notes on field theory in condensed matter physics
5.5
Problems
... ...................... 247
5.5.1
Equal
Ume
non-interacting two-point Green function for a
Ferro.)
gas
........................... 247
5.5.2
Application of the
Kubo
formula to the Hall conductivity
in the .integer quantum Hall effect
.............. 24.8
5.5.3
The Hall conductivity and gauge
invariance
......... 252
6.
Jeliium model for elect.ro.ns in a solid
259
6.1
Introduction
................................ 259
6.2
Definition
oí
the Coulomb gas in the
Schrödinger
picture
...... 260
6.2.1
The classical three-dimensional Coulomb gas
........ 260
6.2.2
The quantum three-dimensional Coulomb gas
....... 261
6.3
Path-integral representation of the Coulomb gas
.......... 264
6.4
The random phase approximation
................. 266
6.4.1
PI.ubbard
■
Stratonovich transformation
............ 266
6.4.2
Integration of the electrons
.................. 268
6.4.3
Gaussian expansion of the fermiornc determinant
..... 268
6.5
Diagrammatic interpretation of the random phase
approximation
............................. 272
6 6
Ground-state energy in the random-phase approximation
. . . . 275
6.7 Lind
hard response function
....................... 276
6.7.1
Pong wavelength and quasi-static limit at
Τ
- 0...... 283
6.7.2
Long-wavelength and dynamic limit at
Τ
— 0........ 290
6.8
Random-phase approximation for a short-range interaction
.... 291
6.9
Feedback effect on and by phonons
.................. 293
6.10
Problems
..................... ...... 295
6.10.1
Static Lindhard function in one· dimensional position space
295
6.1.0.2
Puttinger theorem revisited: Adiabatic flux insertion
. . . 297
610.3
Fermionic slave particles
................... 305
7.
Superconductivity
m
the mean-field and random-phase approximations
317
7.1
Pairing-order parameter
........................ 317
7.1.1
Phase operator
......................... 319
7.1.2
Center-of mass and relative coordinates
........... 322
7.2
Scaling of electronic interactions
.................. 323
7.2.1
Case of a repulsive interaction
................ 323
7.2.2
Case of an attractive interaction
............... 331
7.3
Time- and space-independent Landau- Girrzburg action
....... 332
7.3.1
Effective potential at
Τ
= 0............. 334
7.3.2
Effective free energy in the vicinity of 2 c
........ 336
7.4
Mean-field theory oC superconductivity
................ 339
7.5
Nambu-
Gorkov representation
...................... 344
Contents xvjj
7.6
E
flecti
ve
action for the pairing-order parameter
........... 346
7.7
Effective theory in the vicinity of T
-- 0............ 347
7.7.1
Spadai twist
around
,Δ
................. 348
7.7.2
Time twist around
,Δ
.................... 353
7.7.3
Conjectured low energy action tor the pha.se of trie condensate3b4
7.7.4
Polarization tensor for a BGS superconductor
...... 357
7.8
Effective theory in the vicinity of
Τ
=
Tr
............. . . 367
7.9
Problems
.............................. 372
7.9.1
BCS variational method to superconductivity
..... 372
7.9.2
Flux quantization in a superconductor
........... 374
7.9.3
Collective excitations within the
RPA
approximation
. 375
7.9.4
The HalJ conductivity in a superconductor and gauge
invariance
........................... 378
8,
A single dissipative
Josephson
junction
379
8.1
Pnenomenological model of
a Josephson
junction
.......... 379
8.2
DC-
Josephson
effect
............ . . , 384
8.3
AC-
Josephson
effect
...... ........ ..... 384
8.4
Dissipative
Josephson
junction
.... ... 385
8.4.1
Classical
................... . . 385
8.4.2
Caldeira-Leggett model
............... 387
8.5
In.stan.tons in quantum mechanics
............ . 396
8.5.1
Introduction
.............. ....... 396
8.5 2
Serai-
classical approximation within the Euclidean path-
integral representation of quantum mechanics
...... 397
8.5.3
Application to a parabolic potential well
.......... 400
8.5.4
Application to the double well potential
.......... 402
8.5.5
Application to the periodic potential
............ 410
8.5
б
The case of an. unbounded potential of the cubic type
, . . 412
8.6
The quantum dissipative
Josephson
junction
............. 417
8.7
Duality ui a dissipative
Josephson
junction
........... 422
8.7.1
Regime
m y
<ŽC
1
and my
<íC
η...............
422
8 7.2
Regime my»
1
and
m y
:»
η
..... . . . . 426
8.7.3
Duality
,
... ...... ... . ...
,
430
8.8
Renormalization-gToup methods
................... 431
8.8.1
Diffusive .regime when my <iC
1
and my <<C
η
....... 431
8.8.2
Diffusive
regime when my 2>
1
and rn
y
3>
η
...... 435
8.9
Conjectured phase diagram for a. dissipative
Josephson
junction
.........................-..... 436
8.10
Problems
........ ... ...... 438
810 1
The Kondo effect: A perturbatrve approach
. ..... 438
8.10.2
The Kondo effect: A non-perturbative approach
..... 445
xviii
Lecture notes on field theory in condensed matter physics
9.
Abel i
an bosonjzation in two-dimensional space and time
473
9.1
introduction
............................... 473
9.2
/Ybelian bosonization of the Thirrmg model
........... 475
9.2.1
Free-field fixed point
m
the massive Thirrmg model
.... 475
9.2.2
The
ry( l)
axial-gauge anomaly
................ 480
9.2.3
Abelian bosonization of the mass less Thirrmg
modei
.... 4.86
9.2.4
Abelian bosonizaLion of the massive Thirrmg model
.... 491
9.3
Applications
. .......................... 492
9-3.1
Spmless
fermions
with effective
Lorentz
and global
U
(I)
gauge symmetries
....................... 492-
9.3.2
Quantum xxz spin-
1/2
chain
................ 497
9.3.3
Single impurity of the mass type
............... 507
9.4
Problems
................................ 510
9.4.1
Quantum chiral edge theory
................. 510
9.4.2
Two- point correlation function in. the massless Thirring
model
..........................- . . 520
Appendix A The harmonic-oscillator algebra, and its coherent states
529
A.I The harmonic oscillator algebra and its coherent states
....... 529
A.
1.1
Bosonic algebra
.................... . . . 529
A.
1.2
Coherent states
........................ 530
A.
2
Path-integral representation of the anharmonic oscillator
...... 533
A..3 Higher dimensional generalizations
.................. 536
Appendix
В
Some Gaussian integrals
539
H.I Generating function
.......................... 539
B.2
Bose-
Einstein distribution and the residue theorem
.......... 540
Appendix
С
Non-Linear Sigma Models (NLaM) on Riemarmian manifolds
543
C.I. Introduction
................................ 543
C.2 A few preliminary definitions
..................... 543
C-3 Definition of a NLcM on a Riemannian manifold
.......... 546
C.4 Classical equations of motion, for NLaM:
Christoffel
symbol and geodesies
................... 548
С
5
Riemann.
Fücci,
and scalar curvature tensors
............ 550
C-6 Normal coordinates and vielbeins for NLcrM
........... 557
С
6.1.
The background held method
................ 557
С
6-2
A mathematical excursion
.................. 558
C-6.3 Normal coordinates for NLaM
............... 560
С
6.4
Gaussian expansion of the action
.............. 566
Сб.
5
Diagonalization of the metric tensor through vielbeins
, . . 568
Contants
xix
С.
6.6
llenormalization
of the action after integration over the fast
degrees of freedom
....................... 572
G.6.7 One loop scaling flow obeyed by
che
metric tensor
..... 576
C.7 ITow many couplings flow on a NLcM?
................ 577
Appendix
D
The
Viliam
model
579
Appendix
Ľ
Coherent states for
fermions, Jordan-Wigner fermions,
and linear-response theory
585
E.I Grassma.n.n coherent states
...................... 585
E.2 Path-integral representation Tor
fermions
............... 588
Ľ.3
Jordan-Wigner
fermions
....................... 590
E.
3.1
Introduction
.......................... 590
E.
3.2
Nearest-neighbor and quantum xy limit in one-dimensional
position, space
......................... 592
E.4- The ground state energy and the single-particle time ordered Green
function
.............................. 599
E.5 Linear response
......................... 604
E.5.1 Introduction
........................ 604
E.5.
2
The
Kubo
formula
...................... 605
E
5 3
Kubo
formula for the conductivity
............ 608
E.5-4
Kubo
formula for the do conductance
........... 612
E.5.
5
Kubo
formula for the dielectric function
........... 614
E.5.
6
Fluctuation-dissipation theorem
............... 616
Appendix
F
Landau theory of Fermi liquids
621
FM
Adiabatic continuity
.......................... 621.
F.2 Quasiparticles
............................ 623
F.3
Topologica!
stability of the Fermi surface
.............. 626
F.3-1 The case of no many body interactions
........... 626
F.3.
2
The case with many body interactions
.......... 629
F.4 Quasiparticles in the Landau theory of Fermi liquids as poles of the
two-point Green function
..................... 634
F.5 Breakdown of Landau Fermi liquid theory
............. 635
F
5.1
Gapped phases
........................ 635
F.5.
2
Luttinger liquids
.............. ... 635
Appendix
G
First-order phase transitions induced by thermal .fluctuations
639
G.I Landau Gmzburg theory and the mean Reid theory of continuous
phase transitions
......................... 639
G.2 Fluctuations induced by a local gauge symmetry
.......... 644
G.3 Applications
............................ 650
X.X
Lecture notes on
field
Ĺheory
гп
condensed matter physics
Appendix. II Useful identities
653
II.
1
Proof of Equation
(8.75)........................ 653
НМЛ
Proof of Eq.
(Ы.5)
. .......... 653
II
1.2
Proof of Eq. (H.ll)
...................... 654
H.1.3 Proof of Pq. (II
22)..................... 657
H.1.-1 Proof of Eq. (H..28)
...... ... 658
III.
5
Proof of Eq. (H
31}...................... 658
H.I.
6
Proof of Eq.
(11.40) . ........... 660
I
Non-
Abelian bosonization
661
Introduction
................................ 661
VTinkowski versus Euclidean spaces
................. 661
Free massless Dirac
fermions
and the Wcss
Zum
і
no-
W
it ten theory
664
A quantum mechanical example of a, Wess-Zummo action
..... 673
VVess-
Zumino
action in
(1
+l)-dimensional Minkowski space and tirne677
Equations of motion for the WZNW action
............. 680
One-loop RG fiow for the WZNW theory
............. 685
The Polyakov-Wiegrna.nn identity
................ . . 687
Integration of the anomaly in Q(yl)2
................ 687
1.9.1
General symmetry considerations
.............- 687
1.9.2
The axial gauge anomaly for QCD2
........... 694
I
10
Bosonization of QCD2 for mlir.ute.ly strong gauge coupling
. 702
Bibliography
Index
Appendix
I
1
.1
.2
I
3
I
4
I
5
I.
6
I
7
I.
8
I.
9
LECTURE NOTES ON
FIELD THEORY IN
ENSED MATTER PHYSICS
The aim of this book is to introduce a graduate student to selected
concepts in condensed matter physics for which the language
of field theory is ideally suited. The examples considered in
this book are those of superfluidity for weakly interacting
bosons, cofl¡near magnetism, and superconductivity. Quantum
phase transitions are also treated in the context of quantum
díssipatíve
junctions and interacting
fermions
constrained to
one-dimensional position space. The style of presentation is
sufficiently detailed and comprehensive that it only presumes
familiarity with undergraduate physics.
|
| any_adam_object | 1 |
| author | Mudry, Christopher 1975- |
| author_GND | (DE-588)1051266327 |
| author_facet | Mudry, Christopher 1975- |
| author_role | aut |
| author_sort | Mudry, Christopher 1975- |
| author_variant | c m cm |
| building | Verbundindex |
| bvnumber | BV041437844 |
| classification_rvk | SK 300 UO 4000 UP 1300 |
| classification_tum | PHY 023f PHY 602f |
| ctrlnum | (OCoLC)880357849 (DE-599)BVBBV041437844 |
| discipline | Physik Mathematik |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV041437844 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:56:41Z |
| institution | BVB |
| isbn | 9789814449090 9814449091 9789814449106 9814449105 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026884671 |
| oclc_num | 880357849 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-29T DE-20 DE-91G DE-BY-TUM DE-11 |
| owner_facet | DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-29T DE-20 DE-91G DE-BY-TUM DE-11 |
| physical | xx, 724 Seiten Illustrationen |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Mudry, Christopher 1975- Verfasser (DE-588)1051266327 aut Lecture notes on field theory in condensed matter physics Christopher Mudry (Paul Scherrer Institut, Switzerland) New Jersey World Scientific [2014] xx, 724 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Festkörper (DE-588)4016918-2 gnd rswk-swf Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Kondensierte Materie (DE-588)4132810-3 gnd rswk-swf Feldtheorie (DE-588)4016698-3 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Kondensierte Materie (DE-588)4132810-3 s Quantenfeldtheorie (DE-588)4047984-5 s DE-604 Festkörper (DE-588)4016918-2 s Feldtheorie (DE-588)4016698-3 s Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026884671&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026884671&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Mudry, Christopher 1975- Lecture notes on field theory in condensed matter physics Festkörper (DE-588)4016918-2 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd Kondensierte Materie (DE-588)4132810-3 gnd Feldtheorie (DE-588)4016698-3 gnd |
| subject_GND | (DE-588)4016918-2 (DE-588)4047984-5 (DE-588)4132810-3 (DE-588)4016698-3 (DE-588)4123623-3 |
| title | Lecture notes on field theory in condensed matter physics |
| title_auth | Lecture notes on field theory in condensed matter physics |
| title_exact_search | Lecture notes on field theory in condensed matter physics |
| title_full | Lecture notes on field theory in condensed matter physics Christopher Mudry (Paul Scherrer Institut, Switzerland) |
| title_fullStr | Lecture notes on field theory in condensed matter physics Christopher Mudry (Paul Scherrer Institut, Switzerland) |
| title_full_unstemmed | Lecture notes on field theory in condensed matter physics Christopher Mudry (Paul Scherrer Institut, Switzerland) |
| title_short | Lecture notes on field theory in condensed matter physics |
| title_sort | lecture notes on field theory in condensed matter physics |
| topic | Festkörper (DE-588)4016918-2 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd Kondensierte Materie (DE-588)4132810-3 gnd Feldtheorie (DE-588)4016698-3 gnd |
| topic_facet | Festkörper Quantenfeldtheorie Kondensierte Materie Feldtheorie Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026884671&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026884671&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT mudrychristopher lecturenotesonfieldtheoryincondensedmatterphysics |