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

by Chaichian; M

• ISBN13: 9780750308021
• ISBN10: 0750308028
• Format: Hardcover
• Copyright: 2001-07-01
• Publisher: CRC Press

Summary

Devoted to quantum field theory and statistical physics. Deals with systems with an infinite number of degrees of freedom.

Table of Contents

Preface to volume II	ix
Quantum field theory: the path-integral approach	1	(193)
Path-integral formulation of the simplest quantum field theories	2	(47)
Systems with an infinite number of degrees of freedom and quantum field theory	2	(12)
Path-integral representation for transition amplitudes in quantum field theories	14	(7)
Spinor fields: quantization via path integrals over Grassmann variables	21	(1)
Perturbation expansion in quantum field theory in the path-integral approach	22	(5)
Generating functionals for Green functions and an introduction to functional methods in quantum field theory	27	(11)
Problems	38	(11)
Path-integral quantization of gauge-field theories	49	(52)
Gauge-invariant Lagrangians	50	(4)
Constrained Hamiltonian systems and their path-integral quantization	54	(6)
Yang-Mills fields: constrained systems with an infinite number of degrees of freedom	60	(4)
Path-integral quantization of Yang-Mills theories	64	(3)
Covariant generating functional in the Yang-Mills theory	67	(6)
Covariant perturbation theory for Yang-Mills models	73	(7)
Higher-order perturbation theory and a sketch of the renormalization procedure for Yang-Mills theories	80	(8)
Spontaneous symmetry-breaking of gauge invariance and a brief look at the standard model of particle interactions	88	(10)
Problems	98	(3)
Non-perturbative methods for the analysis of quantum field models in the path-integral approach	101	(48)
Rearrangements and partial summations of perturbation expansions: the 1/N-expansion and separate integration over high and low frequency modes	101	(9)
Semiclassical approximation in quantum field theory and extended objects (solitons)	110	(10)
Semiclassical approximation and quantum tunneling (instantons)	120	(10)
Path-integral calculation of quantum anomalies	130	(7)
Path-integral solution of the polaron problem	137	(7)
Problems	144	(5)
Path integrals in the theory of gravitation, cosmology and string theory: advanced applications of path integrals	149	(45)
Path-integral quantization of a gravitational field in an asymptotically flat spacetime and the corresponding perturbation theory	149	(5)
Path integrals in spatially homogeneous cosmological models	154	(6)
Path-integral calculation of the topology-change transitions in (2 + 1)-dimensional gravity	160	(6)
Hawking's path-integral derivation of the partition function for black holes	166	(8)
Path integrals for relativistic point particles and in the string theory	174	(11)
Quantum field theory on non-commutative spacetimes and path integrals	185	(9)
Path integrals in statistical physics	194	(117)
Basic concepts of statistical physics	195	(5)
Path integrals in classical statistical mechanics	200	(5)
Path integrals for indistinguishable particles in quantum mechanics	205	(18)
Permutations and transition amplitudes	206	(4)
Path-integral formalism for coupled identical oscillators	210	(6)
Path integrals and parastatistics	216	(5)
Problems	221	(2)
Field theory at non-zero temperature	223	(34)
Non-relativistic field theory at non-zero temperature and the diagram technique	223	(3)
Euclidean-time relativistic field theory at non-zero temperature	226	(7)
Real-time formulation of field theory at non-zero temperature	233	(5)
Path integrals in the theory of critical phenomena	238	(7)
Quantum field theory at finite energy	245	(7)
Problems	252	(5)
Superfluidity, superconductivity, non-equilibrium quantum statistics and the path-integral technique	257	(23)
Perturbation theory for superfluid Bose systems	258	(3)
Perturbation theory for superconducting Fermi systems	261	(2)
Non-equilibrium quantum statistics and the process of condensation of an ideal Bose gas	263	(14)
Problems	277	(3)
Non-equilibrium statistical physics in the path-integral formalism and stochastic quantization	280	(15)
A zero-dimensional model: calculation of usual integrals by the method of `stochastic quantization'	281	(3)
Real-time quantum mechanics within the stochastic quantization scheme	284	(4)
Stochastic quantization of field theories	288	(5)
Problems	293	(2)
Path-integral formalism and lattice systems	295	(16)
Ising model as an example of genuine discrete physical systems	296	(6)
Lattice gauge theory	302	(6)
Problems	308	(3)
Supplements	311	(21)
Finite-dimensional Gaussian integrals	311	(2)
Table of some exactly solved Wiener path integrals	313	(3)
Feynman rules	316	(1)
Short glossary of selected notions from the theory of Lie groups and algebras	316	(9)
Some basic facts about differential Riemann geometry	325	(4)
Supersymmetry in quantum mechanics	329	(3)
Bibliography	332	(5)
Index	337