Dynamics of classical and quantum fields: an introduction
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, Fla. [u.a.]
CRC Press
2014
|
| Subjects: | |
| Online Access: | Klappentext Inhaltsverzeichnis |
| Physical Description: | XVII, 370 p. Ill |
| ISBN: | 9781466556287 1466556285 |
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MARC
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| 245 | 1 | 0 | |a Dynamics of classical and quantum fields |b an introduction |c Girish S. Setlur |
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| 300 | |a XVII, 370 p. |b Ill | ||
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Record in the Search Index
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| adam_text | Contents
List of Figures
xi
Preface
xiii
About the Author
xvii
1
The Countable and the Uncountable
1
1.1
Review of Lagrangian Mechanics
................. 1
1.2
The Hamiltonian Formulation
................... 8
1.3
Rows and Symmetries
....................... 11
1.4
Dynamics of a Continuous System
................. 13
1.5
Variational Methods
........................ 23
1.5.1
The Brachistochrone Problem
............... 24
1.5.2
Fermaťs
Principle in Optics
................ 28
1.5.3
Least Square Fit
...................... 32
1.6
Exercises
.............................. 35
2
Symmetries and Noether s Theorem
41
2.1
Noether s Theorem in a Lagrangian Setting
............ 42
2.2
Noether s Theorem in a Hamiltonian Setting
............ 46
2.3
Dynamical Symmetries
....................... 46
2.4
Symmetries in Field Theories
................... 48
2.5
Exercises
.............................. 54
3
The Electromagnetic Field and Stress Energy Tensor
55
3.1
Relativistic Nature of the Electromagnetic Field
.......... 55
3.2
Lagrangian of the EM Field
..................... 63
3.2.1
Gauge Symmetry and Conservation Laws
......... 66
3.3
Stress Energy Tensor of the EM Field
............... 67
3.4
Solution of Maxwell s Equations Using Green s Functions
.... 75
3.4.1
Gauss s Law in Electrostatics
............... 77
3.4.2
Lienard-Wiechert Potentials
................ 82
vu
viii Contents
3.5
Diffraction
Theory
......................... 86
3.6
Exercises
.............................. 95
4
Elasticity
Theory and Fluid Mechanics
99
4.1
Stress and Strain Tensor of Deformable Bodies
.......... 99
4.1.1
Stress
............................ 99
4.1.2
Strain
............................ 101
4.1.3
The Stress Function Method
................ 103
4.2
Strain Energy
............................ 112
4.3
Euler
and
Navier
Stokes Equations
................ 114
4.3.1
Equation of Continuity and Current Algebra
....... 114
4.3.2
The
Euler
Equation
.................... 119
4.4
Bernoulli s Equation for an Incompressible Fluid
......... 123
4.5
Navier
Stokes Equation
...................... 125
4.6
Conserved Quantities and Dissipation Rates
............ 126
4.7
Turbulence
............................. 128
4.8
Exercises
.............................. 141
5
Toward Quantum Fields: Scalar and Spinor Fields
145
5.1
Some Solutions of the Schrodinger Equation
............ 149
5.2
Some Properties of the Dirac Equation and Klein Gordon Equations
154
5.3
Exercises
.............................. 157
6
Concept of Functional Integration
159
6.1
Integration over Functions
..................... 159
6.2
Perturbation Theory
........................ 163
6.3
Exercises
.............................. 166
7
Quantum Mechanics Using Lagrangjans: Path Integrals
169
7.1
The Formalism
........................... 169
7.2
Free Particles
............................ 174
7.2.1
Free Particle
........................ 174
7.2.2
Free
Fermions
....................... 176
7.3
Harmonic Oscillator
........................ 183
7.4
Two-Particle Green Functions
................... 185
7.5
Exercises
.............................. 187
8
Creation and Annihilation Operators in Fock Space
189
8.1
Introduction to Second Quantization
................ 189
8.1.1
The Quantum Electromagnetic Field
........... 192
8.2
Creation and Annihilation Operators in Many-Body Physics
... 196
8.3
Green Functions in Many-Body Physics
.............. 201
8.4
Hamiltonians Using Creation and Annihilation Operators
..... 203
Contents ix
8.5
Current
Algebra........................... 205
8.6
Exercises
.............................. 208
9 Quantum
Fields on a Lattice
209
9.1
Derivation of the Tight Binding Picture
.............. 210
9.2
Schrieffer-Wolff Transformation
.................. 219
9.3
Exercises
.............................. 223
10
Green Functions: Matsubara and Nonequilibrium
225
10.1
Matsubara Green Functions
.................... 225
10.2
Nonequilibrium Green Functions
................. 235
10.3
Schwinger-Dyson Equations
.................... 241
10.4
Exercises
.............................. 254
11
Coherent State Path Integrals
257
11.1
CSPI for a Harmonic Oscillator
................... 257
11.1.1
Evaluation of the Path Integral
............... 261
11.2
CSPI for a Fermionic Oscillator
.................. 265
11.2.1
Evaluating the Path Integral
................ 269
11.3
Generalization to Fields
...................... 271
11.4
Exercises
.............................. 272
12
Nonlocal Operators
273
12.1
Quantum Vortices in a Charged Boson Fluid
............ 273
12.2
Nonlocal Particle Hole Creation Operators
............ 279
12.2.1
A Systematic Approach for Going beyond
RPA
..... 281
12.3
The Sea-Boson
........................... 287
12.3.1
Asymptotically Exact Momentum
Distribution for Forward Scattering Interactions
..... 296
12.3.2
Short-Range Interactions
................. 296
12.3.3
Long-Range Interactions
.................. 299
12.4
Exercises
.............................. 300
13
Non-chiral Bosonization of
Fermions
in One Dimension
303
13.1
A Critique of Conventional Chiral Bosonization
.......... 304
13.1.1
Chiral
Fermions on a
Ring
................. 306
13.2
General Considerations
....................... 316
13.2.1
Free Propagator and Luttinger Liquid
........... 321
13.3
Impurity in a Luttinger Liquid
................... 326
13.3.1
Anomalous Scaling
.................... 328
13.3.2
The Field Operator Construction
............. 330
13.4
Closed Form for Full Propagator
.................. 335
x
Contents
13.4.1 Transport
across the Impurity
............... 338
13.5
Exercises
.............................. 338
Bibliography
341
Index
363
Physics
namical fields in non-relativistic physics. Written by a physicist for physicists,
the book is designed to help readers develop analytical skills related to classical
and quantum fields at the non-relativistic level, and think about the concepts
and theory through numerous problems. In-depth yet accessible, the book pres¬
ents new and conventional topics in a self-contained manner that beginners
would find useful. A partial list of topics covered includes:
•
Geometrical meaning of Legendre transformation in classical mechanics
•
Dynamical symmetries in the context of Noether s theorem
•
The derivation of the stress energy tensor of the electromagnetic field,
the expression for strain energy in elastic bodies, and the
Navier
Stokes
equation
•
Concepts of right and left movers in case of a Fermi gas explained
•
Functional integration interpreted as a limit of a sequence of ordinary
integrations
•
Path integrals for one and two quantum particles and for a fermion in
presence of a filled Fermi sea
•
Fermion and boson Fock spaces, along with operators that create and
annihilate particles
•
Coherent state path integrals
•
Many-body topics such as Schrieffer Wolff transformation, Matsubara, and
Keldysh Green functions
•
Geometrical meaning of the vortex-vortex correlation function in a charged
boson fluid
•
Nonlocal particle-hole creation operators which diagonalize interacting
many-body systems
The equal mix of novel and traditional topics, use of fresh examples to illustrate
conventional concepts, and large number of worked examples make this
book ideal for an intensive one-semester course for beginning Ph.D. students.
It is also a challenging and thought provoking book for motivated advanced
underqraduates.
|
| any_adam_object | 1 |
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| spelling | Setlur, Girish S. 1968- Verfasser (DE-588)104935267X aut Dynamics of classical and quantum fields an introduction Girish S. Setlur Boca Raton, Fla. [u.a.] CRC Press 2014 XVII, 370 p. Ill txt rdacontent n rdamedia nc rdacarrier Dynamisches System (DE-588)4013396-5 gnd rswk-swf Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Feldtheorie (DE-588)4016698-3 gnd rswk-swf Feldtheorie (DE-588)4016698-3 s Dynamisches System (DE-588)4013396-5 s DE-604 Quantenfeldtheorie (DE-588)4047984-5 s Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027219470&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Klappentext Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027219470&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Setlur, Girish S. 1968- Dynamics of classical and quantum fields an introduction Dynamisches System (DE-588)4013396-5 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd Feldtheorie (DE-588)4016698-3 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4047984-5 (DE-588)4016698-3 |
| title | Dynamics of classical and quantum fields an introduction |
| title_auth | Dynamics of classical and quantum fields an introduction |
| title_exact_search | Dynamics of classical and quantum fields an introduction |
| title_full | Dynamics of classical and quantum fields an introduction Girish S. Setlur |
| title_fullStr | Dynamics of classical and quantum fields an introduction Girish S. Setlur |
| title_full_unstemmed | Dynamics of classical and quantum fields an introduction Girish S. Setlur |
| title_short | Dynamics of classical and quantum fields |
| title_sort | dynamics of classical and quantum fields an introduction |
| title_sub | an introduction |
| topic | Dynamisches System (DE-588)4013396-5 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd Feldtheorie (DE-588)4016698-3 gnd |
| topic_facet | Dynamisches System Quantenfeldtheorie Feldtheorie |
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