Quantum Field Theory And Topology Book

	Introduction	1
	Definitions and Notations	6
1	The Simplest Lagrangians	13
2	Quadratic Lagrangians	17
3	Internal Symmetries	19
4	Gauge Fields	24
5	Particles Corresponding to Nonquadratic Lagrangians	28
6	Lagrangians of Strong, Weak and Electromagnetic Interactions	30
7	Grand Unifications	37
8	Topologically Stable Defects	43
9	Topological Integrals of Motion	56
10	A Two-Dimensional Model. Abrikosov Vortices	62
11	't Hooft-Polyakov Monopoles	68
12	Topological Integrals of Motion in Gauge Theory	74
13	Particles in Gauge Theories	80
14	The Magnetic Charge	83
15	Electromagnetic Field Strength and Magnetic Charge in Gauge Theories	89
16	Extrema of Symmetric Functionals	94
17	Symmetric Gauge Fields	97
18	Estimates of the Energy of a Magnetic Monopole	104
19	Topologically Non-Trivial Strings	109
20	Particles in the Presence of Strings	115
21	Nonlinear Fields	122
22	Multivalued Action Integrals	128
23	Functional Integrals	132
24	Applications of Functional Integrals to Quantum Theory	138
25	Quantization of Gauge Theories	146
26	Elliptic Operators	158
27	The Index and Other Properties of Elliptic Operators	163
28	Determinants of Elliptic Operators	169
29	Quantum Anomalies	173
30	Instantons	183
31	The Number of Instanton Parameters	194
32	Computation of the Instanton Contribution	199
33	Functional Integrals for a Theory Containing Fermion Fields	207
34	Instantons in Quantum Chromodynamics	216
35	Topological Spaces	223
36	Groups	225
37	Gluings	229
38	Equivalence Relations and Quotient Spaces	233
39	Group Representations	235
40	Group Actions	241
41	The Adjoint Representation of a Lie Group	245
42	Elements of Homotopy Theory	247
43	Applications of Topology to Physics	257
	Bibliographical Remarks	261
	References	263
	Index	269