Path Integrals in Physics: Volume II Quantum Field Theory, Statistical Physics and other Modern Applications

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CRC Press, Jul 1, 2001 - Science - 346 pages
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The path integral approach has proved extremely useful for the understanding of the most complex problems in quantum field theory, cosmology, and condensed matter physics. Path Integrals in Physics: Volume II, Quantum Field Theory, Statistical Physics and other Modern Applications covers the fundamentals of path integrals, both the Wiener and Feynman types, and their many applications in physics. The book deals with systems that have an infinite number of degrees of freedom. It discusses the general physical background and concepts of the path integral approach used, followed by a detailed presentation of the most typical and important applications as well as problems with either their solutions or hints how to solve them. Each chapter is self-contained and can be considered as an independent textbook. It provides a comprehensive, detailed, and systematic account of the subject suitable for both students and experienced researchers.
  

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Contents

Quantum field theory the pathintegral approach
1
311 Systems with an infinite number of degrees of freedom and quantum field theory
2
312 Pathintegral representation for transition amplitudes in quantum field theories
14
quantization via path integrals over Grassmann variables
21
314 Perturbation expansion in quantum field theory in the pathintegral approach
22
315 Generating functionals for Green functions and an introduction to functional methods in quantum field theory
27
316 Problems
38
32 Pathintegral quantization of gaugefield theories
49
431 Permutations and transition amplitudes
206
432 Pathintegral formalism for coupled identical oscillators
210
433 Path integrals and parastatistics
216
434 Problems
221
441 Nonrelativistic field theory at nonzero temperature and the diagram technique
223
442 Euclideantime relativistic field theory at nonzero temperature
226
443 Realtime formulation of field theory at nonzero temperature
233
444 Path integrals in the theory of critical phenomena
238

321 Gaugeinvariant Lagrangians
50
322 Constrained Hamiltonian systems and their pathintegral quantization
54
constrained systems with an infinite number of degrees of freedom
60
324 Pathintegral quantization of YangMills theories
64
325 Covariant generating functional in the YangMills theory
67
326 Covariant perturbation theory for YangMills models
73
327 Higherorder perturbation theory and a sketch of the renormalization procedure for Yang Mills theories
80
328 Spontaneous symmetrybreaking of gauge invariance and a brief look at the standard model of particle interactions
88
329 Problems
98
331 Rearrangements and partial summations of perturbation expansions the I N expansion and separate integration over high and low frequency mo...
101
332 Semiclassical approximation in quantum field theory and extended objects solitons
110
333 Semiclassical approximation and quantum tunneling instantons
120
334 Pathintegral calculation of quantum anomalies
130
335 Pathintegral solution of the polaron problem
137
336 Problems
144
advanced applications of path integrals 341 Pathintegral quantization of a gravitational field in an asymptotically flat spacetime and the correspondin...
149
342 Path integrals in spatially homogeneous cosmological models
154
343 Pathintegral calculation of the topologychange transitions in 2 + 1dimensional gravity
160
344 Hawkings pathintegral derivation of the partition function for black holes
166
345 Path integrals for relativistic point particles and in the string theory
174
346 Quantum field theory on noncommutative spacetimes and path integrals
185
Path integrals in statistical physics
194
41 Basic concepts of statistical physics
195
42 Path integrals in classical statistical mechanics
200
43 Path integrals for indistinguishable particles in quantum mechanics
205
445 Quantum field theory at finite energy
245
446 Problems
252
45 Superfluidity superconductivity nonequilibrium quantum statistics and the pathintegral technique
257
451 Perturbation theory for superfluid Bose systems
258
452 Perturbation theory for superconducting Fermi systems
261
453 Nonequilibrium quantum statistics and the process of condensation of an ideal Bose gas
263
454 Problems
277
46 Nonequilibrium statistical physics in the pathintegral formalism and stochastic quantization
280
calculation of usual integrals by the method of stochastic quantization
281
462 Realtime quantum mechanics within the stochastic quantization scheme
284
463 Stochastic quantization of field theories
288
464 Problems
293
47 Pathintegral formalism and lattice systems
295
471 Ising model as an example of genuine discrete physical systems
296
472 Lattice gauge theory
302
473 Problems
308
I Finitedimensional Gaussian integrals
311
II Table of some exactly solved Wiener path integrals
313
IV Short glossary of selected notions from the theory of Lie groups and algebras
316
V Some basic facts about differential Riemann geometry
325
VI Supersymmetry in quantum mechanics
329
Bibliography
332
Index
337
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About the author (2001)

Chaichian, University of Helsinki.

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