Polyakov A.M. Gauge Fields and Strings

Harwood Academic Publishers, Chur, London, Paris, New York, Melbourne, 1987. — 310 p.For many years I have been keeping notes on different topics in physics—a kind of scientific diary. They contain occasional new results and mostly derivations of known things, done in a way that seemed nice to me. The notes were very helpful when I needed to recall some subject.
It is surely best to consult with one's own self. This book has arisen from these notes, or better to say, from the part of them devoted to field theory. I decided to publish it because it seems that there are some people who may find it useful. In many cases I discuss things that have never been completely understood. I do this in the hope that the approach I suggest, although imperfect, will stimulate deeper penetration into the subject.Statistical Mechanics and Quantum Field Theory
Quantum Particles
Global and Local Symmetries
Preliminary Description
Discrete Global Symmetries
Continuum Abelian Global Symmetries
Non-Abelian Global Symmetries
Discrete Gauge Symmetries
O(2) Gauge Systems
Non-Abelian Gauge Theories
Asymptotic Freedom and the Renormalization Group
Principal Chiral Fields
The n-Fields
Non-Abelian Gauge Fields for D = 4
The Strong Coupling Expansion
Ising Model
Continuous Global Symmetry
Gauge Symmetries
Instantons in Abelian Systems
Instantons in Quantum Mechanics and the Ising model
Instantons in the Global O(2) Model
Compact QED (O(2) Gauge Model)
Quark Confinement, Superfluidity, Elasticity. Criteria and Analogies
Topology of Gauge Fields and Related Problems
Instantons for D = 2, N = 3n-Fields
Instantons in Non-Abelian Gauge Theories
Qualitative Effects of Instantons
Analogies Between Gauge and Chiral Fields. Loop Dynamics
Non-Abelian Phase Factor
Quantum Theory of Loops
The Large N Expansion
O(N) sigma-Model
The Principal Chiral Field for SU(N)
The CP N-1 n-model
Non-Abelian Gauge Theory
Quantum Strings and Random Surfaces
Mathematical Preliminaries: Summation of Random Paths
Measures in the Space of Metrics and Diffeomorphisms
Closed Paths
General Theory of Random Hypersurfaces
Two-Dimensional Surfaces. Geometrical Introduction
Computation of Functional Integrals
Scattering Amplitudes
Scattering Amplitudes and the Operator
Product Expansion
The Energy-Momentum Tensor in Conformal Quantum Field Theory
Physical States of String Theory in the Critical Dimension
Fermi Particles
Fermionic Strings
Vertex Operators
Attempt at a Synthesis
Long Wave Oscillations of Strings in Critical Dimensions
Possible Applications of Critical Strings
The Three Dimensional Ising Model
The Dirac Equation in the Two Dimensional Ising Model
The Three Dimensional Case
The Loop Equation
Extrinsic Geometry of Strings