Ideas and Methods of Supersymmetry and Supergravity Book

	Preface
1	Mathematical Background	1
1.1	The Poincare group, the Lorentz group	1
1.2	Finite-dimensional representations of Spin(3, 1)	7
1.3	The Lorentz algebra	13
1.4	Two-component and four-component spinors	17
1.5	Representations of the Poincare group	23
1.6	Elements of differential geometry and gravity	32
1.7	The conformal group	45
1.8	The mass-shell field representation	56
1.9	Elements of algebra with supernumbers	68
1.10	Elements of analysis with supernumbers	91
1.11	The supergroup of general coordinate transformations on R[superscript p/q]	106
2	Supersymmetry and Superspace	117
2.0	Introduction: from R[superscript p/q] to supersymmetry	117
2.1	Superalgebras, Grassmann shells and super Lie groups	121
2.2	The Poincare superalgebra	138
2.3	Unitary representation of the Poincare superalgebra	146
2.4	Real superspace R[superscript 4/4] and superfields	155
2.5	Complex superspace C[superscript 4/2], chiral superfields and covariant derivatives	165
2.6	The on-shell massive superfield representations	172
2.7	The on-shell massless superfield representations	181
2.8	From superfields to component fields	186
2.9	The superconformal group	191
3	Field Theory in Superspace	198
3.1	Supersymmetric field theory	198
3.2	Wess-Zumino model	213
3.3	Supersymmetric nonlinear sigma-models	221
3.4	Vector multiplet models	228
3.5	Supersymmetric Yang-Mills theories	233
3.6	Geometric approach to super Yang Mills theories	245
3.7	Classically equivalent theories	257
4	Quantized Superfields	263
4.1	Picture-change operators	263
4.2	Equivalence of component field and superfield perturbation theories	277
4.3	Effective action (super) functional	286
4.4	The Wess-Zumino model: perturbative analysis	297
4.5	Note about gauge theories	316
4.6	Feynman rules for super Yang-Mills theories	328
4.7	Renormalization	338
4.8	Examples of counterterm calculations: an alternative technique	349
4.9	Superfield effective potential	359
5	Superspace Geometry of Supergravity	374
5.1	Gauge group of supergravity and supergravity fields	374
5.2	Superspace differential geometry	390
5.3	Supergeometry with conformal supergravity constraints	404
5.4	Prepotentials	416
5.5	Einstein supergravity	430
5.6	Prepotential deformations	438
5.7	Supercurrent and supertrace	453
5.8	Supergravity in components	461
6	Dynamics in Supergravity	479
6.1	Pure supergravity dynamics	479
6.2	Linearized supergravity	488
6.3	Supergravity-matter dynamical equations	493
6.4	(Conformal) Killing supervectors. Superconformal models	505
6.5	Conformally flat superspaces, anti-de Sitter superspace	519
6.6	Non-minimal supergravity	527
6.7	New minimal supergravity	539
6.8	Matter coupling in non-minimal and new minimal supergravities	548
6.9	Free massless higher superspin theories	553
7	Effective Action in Curved Superspace	572
7.1	The Schwinger-De Witt technique	572
7.2	Proper-time representation for covariantly chiral scalar superpropagator	588
7.3	Proper-time representation for scalar superpropagators	601
7.4	Super Weyl anomaly	607
7.5	Quantum equivalence in superspace	615
	Bibliography	628
	Index	631