Gauge Fields and Strings

by Polyakov;

• ISBN13: 9783718603930
• ISBN10: 3718603934
• Edition: 1st
• Format: Hardcover
• Copyright: 1987-09-14
• Publisher: CRC Press

Table of Contents

Preface to the Series	viii
Preface	ix
Statistical Mechanics and Quantum Field Theory	1	(18)
Quantum Particles	1	(3)
Global and Local Symmetries. Preliminary Description	4	(1)
Discrete Global Symmetries	5	(6)
Continuum Abelian Global Symmetries	11	(2)
Non-Abelian Global Symmetries	13	(1)
Discrete Gauge Symmetries	14	(1)
O(2) Gauge Systems	15	(2)
Non-Abelian Gauge Theories	17	(2)
Asymptotic Freedom and the Renormalization Group	19	(14)
Principal Chiral Fields	19	(8)
The n-Fields	27	(2)
Non-Abelian Gauge Fields for D = 4	29	(4)
The Strong Coupling Expansion	33	(16)
Ising Model	34	(3)
Continuous Global Symmetry	37	(3)
Gauge Symmetries	40	(9)
Instantons in Abelian Systems	49	(24)
Instantons in Quantum Mechanics and the Ising model	49	(5)
Instantons in the Global O(2) Model	54	(8)
Compact QED (O(2) Gauge Model)	62	(11)
Quark Confinement, Superfluidity, Elasticity. Criteria and Analogies	73	(12)
Topology of Gauge Fields and Related Problems	85	(26)
Instantons for D = 2, N = 3n-Fields	85	(7)
Instantons in Non-Abelian Gauge Theories	92	(7)
Qualitative Effects of Instantons	99	(12)
Analogies Between Gauge and Chiral Fields. Loop Dynamics	111	(14)
Non-Abelian Phase Factor	111	(8)
Quantum Theory of Loops	119	(6)
The Large N Expansion	125	(26)
O(N) σ-Model	125	(9)
The Principal Chiral Field for SU(N)	134	(5)
The CPN-1 n-model	139	(5)
Non-Abelian Gauge Theory	144	(7)
Quantum Strings and Random Surfaces	151	(102)
Mathematical Preliminaries: Summation of Random Paths	151	(6)
Measures in the Space of Metrics and Diffeomorphisms	157	(7)
Closed Paths	164	(5)
General Theory of Random Hypersurfaces	169	(7)
Two-Dimensional Surfaces. Geometrical Introduction	176	(9)
Computation of Functional Integrals	185	(7)
Scattering Amplitudes	192	(3)
Scattering Amplitudes and the Operator Product Expansion	195	(8)
The Energy-Momentum Tensor in Conformal Quantum Field Theory	203	(9)
Physical States of String Theory in the Critical Dimension	212	(10)
Fermi Particles	222	(6)
Fermionic Strings	228	(12)
Vertex Operators	240	(13)
Attempt at a Synthesis	253	(36)
Long Wave Oscillations of Strings in Critical Dimensions	253	(13)
Possible Applications of Critical Strings	266	(7)
The Three Dimensional Ising Model	273	(10)
The Dirac Equation in the Two Dimensional Ising Model	275	(3)
The Three Dimensional Case. The Loop Equation	278	(5)
Extrinsic Geometry of Strings	283	(6)
Subject Index	289