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Quantum Field Theory

:	Michael V. Sadovskii
:	Quantum Field Theory
:	Walter de Gruyter GmbH& Co.KG
:	9783110270358
:	De Gruyter Studies in Mathematical PhysicsISSN
:	1
:	CHF 136.40
:

:	Theoretische Physik
:	English

:	420
:	Wasserzeichen
:	PC/MAC/eReader/Tablet
:	PDF

< >This book discusses the main concepts of the Standard Model of elementary particles in a compact and straightforward way. The work illustrates the unity of modern theoretical physics by combining approaches and concepts of the quantum field theory and modern condensed matter theory. The inductive approach allows a deep understanding of ideas and methods used for solving problems in this field.

< >Michael V. Sadovskii,Institute for Electrophysics, Russian Academy of Sciences, Russia.

	Preface	5
	1 Basics of elementary particles	13
	1.1 Fundamental particles	13
	1.1.1 Fermions	14
	1.1.2 Vector bosons	15
	1.2 Fundamental interactions	16
	1.3 The Standard Model and perspectives	17
	2 Lagrange formalism. Symmetries and gauge fields	21
	2.1 Lagrange mechanics of a particle	21
	2.2 Real scalar field. Lagrange equations	23
	2.3 The Noether theorem	27
	2.4 Complex scalar and electromagnetic fields	30
	2.5 Yang-Mills fields	36
	2.6 The geometry of gauge fields	42
	2.7 A realistic example - chromodynamics	50
	3 Canonical quantization, symmetries in quantum field theory	52
	3.1 Photons	52
	3.1.1 Quantization of the electromagnetic field	52
	3.1.2 Remarks on gauge invariance and Bose statistics	57
	3.1.3 Vacuum fluctuations and Casimir effect	60
	3.2 Bosons	62
	3.2.1 Scalar particles	62
	3.2.2 Truly neutral particles	66
	3.2.3 CPT-transformations	69
	3.2.4 Vector bosons	73
	3.3 Fermions	75
	3.3.1 Three-dimensional spinors	75
	3.3.2 Spinors of the Lorentz group	79
	3.3.3 The Dirac equation	86
	3.3.4 The algebra of Dirac’s matrices	91
	3.3.5 Plane waves	93
	3.3.6 Spin and statistics	95
	3.3.7 C, P, T transformations for fermions	97
	3.3.8 Bilinear forms	98
	3.3.9 The neutrino	99
	4 The Feynman theory of positron and elementary quantum electrodynamics	105
	4.1 Nonrelativistic theory. Green’s functions	105
	4.2 Relativistic theory	108
	4.3 Momentum representation	112
	4.4 The electron in an external electromagnetic field	115
	4.5 The two-particle problem	122
	5 Scattering matrix	127
	5.1 Scattering amplitude	127
	5.2 Kinematic invariants	130
	5.3 Unitarity	133
	6 Invariant perturbation theory	136
	6.1 Schroedinger and Heisenberg representations	136
	6.2 Interaction representation	137
	6.3 S-matrix expansion	140
	6.4 Feynman diagrams for electron scattering in quantum electrodynamics	147
	6.5 Feynman diagrams for photon scattering	152
	6.6 Electron propagator	154
	6.7 The photon propagator	158
	6.8 The Wick theorem and general diagram rules	161
	7 Exact propagators and vertices	168
	7.1 Field operators in the Heisenberg representation and interaction representation	168
	7.2 The exact propagator of photons	170
	7.3 The exact propagator of electrons	176
	7.4 Vertex parts	180
	7.5 Dyson equations	184
	7.6 Ward identity	185
	8 Some applications of quantum electrodynamics	187
	8.1 Electron scattering by static charge: higher order corrections	187
	8.2 The Lamb shift and the anomalous magnetic moment	192
	8.3 Renormalization - how it works	197
	8.4 “Running” the coupling constant	201
	8.5 Annihilation of e+e~ into hadrons. Proof of the existence of quarks	203
	8.6 The physical conditions for renormalization	204
	8.7 The classification and elimination of divergences	208
	8.8 The asymptotic behavior of a photon propagator at large momenta .	212
	8.9 Relation between the “bare” and “true” charges	215
	8.10 The renormalization group in QED	219
	8.11 The asymptotic nature of a perturbation series	221
	9 Path integrals and quantum mechanics	223
	9.1 Quantum mechanics and path integrals	223
	9.2 Perturbation theory	231
	9.3 Functional derivatives	237
	9.4 Some properties of functional integrals	238
	10 Functional integrals: scalars and spinors	244
	10.1 Generating the functional for scalar fields	244
	10.2 Functional integration	249
	10.3 Free particle Green’s functions	252
	10.4 Generating the functional for interacting fields	259
	10.5 f4 theory	262
	10.6 The generating functional for connected diagrams	269
	10.7 Self-energy and vertex functions	272
	10.8 The theory of critical phenomena	276
	10.9 Functional methods for fermions	289
	10.10 Propagators and gauge conditions in QED	297
	11 Functional integrals: gauge fields	299
	11.1 Non-Abelian gauge fields and Faddeev-Popov quantization	299
	11.2 Feynman diagrams for non-Abelian theory	305
	12 The Weinberg-Salam model	314
	12.1 Spontaneous symmetry-breaking and the Goldstone theorem	314
	12.2 Gauge fields and the Higgs phenomenon	320
	12.3 Yang-Mills fields and spontaneous symmetry-breaking	323
	12.4 The Weinberg-Salam model	329
	13 Renormalization	338
	13.1 Divergences in f4	338
	13.2 Dimensional regularization of f4-theory	342
	13.3 Renormalization of f4-theory	347
	13.4 The renormalization group	354
	13.5 Asymptotic freedom of the Yang-Mills theory	360
	13.6 “Running” coupling constants and the “grand unification”	367
	14 Nonperturbative approaches	373
	14.1 The lattice field theory	373
	14.2 Effective potential and loop expansion	385
	14.3 Instantons in quantum mechanics	390
	14.4 Instantons and the unstable vacuum in field theory	401
	14.5 The Lipatov asymptotics of a perturbation series	407
	14.6 The end of the “zero-charge” story?	409
	Bibliography	414
	Index	418