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E-grāmata: Quantum Field Theory

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Quantum Field TheoryPalielināt
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Quantum field theory has been a great success for physics, but it is difficult for mathematicians to learn because it is mathematically incomplete. Folland, who is a mathematician, has spent considerable time digesting the physical theory and sorting out the mathematical issues in it. Fortunately for mathematicians, Folland is a gifted expositor. The purpose of this book is to present the elements of quantum field theory, with the goal of understanding the behavior of elementary particles rather than building formal mathematical structures, in a form that will be comprehensible to mathematicians. Rigorous definitions and arguments are presented as far as they are available, but the text proceeds on a more informal level when necessary, with due care in identifying the difficulties. The book begins with a review of classical physics and quantum mechanics, then proceeds through the construction of free quantum fields to the perturbation-theoretic development of interacting field theory and renormalization theory, with emphasis on quantum electrodynamics.The final two chapters present the functional integral approach and the elements of gauge field theory, including the Salam-Weinberg model of electromagnetic and weak interactions.
Preface vii
Chapter
1. Prologue		 1
1.1. Linguistic prologue: notation and terminology
1
1.2. Physical prologue: dimensions, units, constants, and particles
5
1.3. Mathematical prologue: some Lie groups and Lie algebras
8
Chapter
2. Review of Pre-quantum Physics		 13
2.1. Mechanics according to Newton and Hamilton
13
2.2. Mechanics according to Lagrange
18
2.3. Special relativity
22
2.4. Electromagnetism
25
Chapter
3. Basic Quantum Mechanics		 33
3.1. The mathematical framework
33
3.2. Quantization
42
3.3. Uncertainty inequalities
51
3.4. The harmonic oscillator
53
3.5. Angular momentum and spin
56
3.6. The Coulomb potential
60
Chapter
4. Relativistic Quantum Mechanics		 65
4.1. The Klein-Gordon and Dirac equations
66
4.2. Invariance and covariance properties of the Dirac equation
70
4.3. Consequences of the Dirac equation
74
4.4. Single-particle state spaces
83
4.5. Multiparticle state spaces
89
Chapter
5. Free Quantum Fields		 97
5.1. Scalar fields
97
5.2. The rigorous construction
105
5.3. Lagrangians and Hamiltonian
107
5.4. Spinor and vector fields
112
5.5. The Wightman axioms
119
Chapter
6. Quantum Fields with Interactions		 123
6.1. Perturbation theory
123
6.2. A toy model for electrons in an atom
128
6.3. The scattering matrix
136
6.4. Evaluation of the S-matrix: first steps
143
6.5. Propagators
147
6.6. Feynman diagrams
154
6.7. Feynman diagrams in momentum space
162
6.8. Cross sections and decay rates
167
6.9. QED, the Coulomb potential, and the Yukawa potential
172
6.10. Compton scattering
177
6.11. The Gell-Mann–Low and LSZ formulas
180
Chapter
7. Renormalization		 191
7.1. Introduction
192
7.2. Power counting
196
7.3. Evaluation and regularization of Feynman diagrams
200
7.4. A one-loop calculation in scalar field theory
206
7.5. Renormalized perturbation theory
211
7.6. Dressing the propagator
214
7.7. The Ward identities
219
7.8. Renormalization in QED: general structure
224
7.9. One-loop QED: the electron propagator
234
7.10. One-loop QED: the photon propagator and vacuum polarization
237
7.11. One-loop QED: the vertex function and magnetic moments
244
7.12. Higher-order renormalization
251
Chapter
8. Functional Integrals		 257
8.1. Functional integrals and quantum mechanics
257
8.2. Expectations, functional derivatives, and generating functionals
265
8.3. Functional integrals and Boson fields
271
8.4. Functional integrals and Fermion fields
278
8.5. Afterword: Gaussian processes
287
Chapter
9. Gauge Field Theories		 291
9.1. Local symmetries and gauge fields
291
9.2. A glimpse at quantum chromodynamics
296
9.3. Broken symmetries
299
9.4. The electroweak theory
303
Bibliography 317
Index 323
Biežāk uzdotie jautājumi par e-grāmatām Biežāk uzdotie jautājumi par e-grāmatām
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