Quantum Field Theory and the Standard 1st Model 1st Edition by Matthew D Schwartz ISBN 1107034736 9781107034730

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ISBN 10: 1107034736
ISBN 13:  9781107034730
Author: Matthew D Schwartz

Quantum Field Theory and the Standard 1st Table of contents:

Part I Field theory
1 Microscopic theory of radiation
1.1 Blackbody radiation
1.2 Einstein coefficients
1.3 Quantum field theory
2 Lorentz invariance and second quantization
2.1 Lorentz invariance
2.2 Classical plane waves as oscillators
2.3 Second quantization
Problems
3 Classical field theory
3.1 Hamiltonians and Lagrangians
3.2 The Euler–Lagrange equations
3.3 Noether’s theorem
3.4 Coulomb’s law
3.5 Green’s functions
Problems
4 Old-fashioned perturbation theory
4.1 Lippmann–Schwinger equation
4.2 Early infinities
Problems
5 Cross sections and decay rates
5.1 Cross sections
5.2 Non-relativistic limit
5.3 e+e− → μ+μ− with spin
Problems
6 The S-matrix and time-ordered products
6.1 The LSZ reduction formula
6.2 The Feynman propagator
Problems
7 Feynman rules
7.1 Lagrangian derivation
7.2 Hamiltonian derivation
7.3 Momentum-space Feynman rules
7.4 Examples
7.A Normal ordering and Wick’s theorem
Problems
Part II Quantum electrodynamics
8 Spin 1 and gauge invariance
8.1 Unitary representations of the Poincaré group
8.2 Embedding particles into fields
8.3 Covariant derivatives
8.4 Quantization and the Ward identity
8.5 The photon propagator
8.6 Is gauge invariance real?
8.7 Higher-spin fields
Problems
9 Scalar quantum electrodynamics
9.1 Quantizing complex scalar fields
9.2 Feynman rules for scalar QED
9.3 Scattering in scalar QED
9.4 Ward identity and gauge invariance
9.5 Lorentz invariance and charge conservation
Problems
10 Spinors
10.1 Representations of the Lorentz group
10.2 Spinor representations
10.3 Dirac matrices
10.4 Coupling to the photon
10.5 What does spin 12 mean?
10.6 Majorana and Weyl fermions
Problems
11 Spinor solutions and CPT
11.1 Chirality, helicity and spin
11.2 Solving the Dirac equation
11.3 Majorana spinors
11.4 Charge conjugation
11.5 Parity
11.6 Time reversal
Problems
12 Spin and statistics
12.1 Identical particles
12.2 Spin-statistics from path dependence
12.3 Quantizing spinors
12.4 Lorentz invariance of the S-matrix
12.5 Stability
12.6 Causality
Problems
13 Quantum electrodynamics
13.1 QED Feynman rules
13.2 γ-matrix identities
13.3 e+e− → μ+μ−
13.4 Rutherford scattering e−p+ → e−p+
13.5 Compton scattering
13.6 Historical note
Problems
14 Path integrals
14.1 Introduction
14.2 The path integral
14.3 Generating functionals
14.4 Where is the iε?
14.5 Gauge invariance
14.6 Fermionic path integral
14.7 Schwinger–Dyson equations
14.8 Ward–Takahashi identity
Problems
Part III Renormalization
15 The Casimir effect
15.1 Casimir effect
15.2 Hard cutoff
15.3 Regulator independence
15.4 Scalar field theory example
Problems
16 Vacuum polarization
16.1 Scalar φ3 theory
16.2 Vacuum polarization in QED
16.3 Physics of vacuum polarization
Problems
17 The anomalous magnetic moment
17.1 Extracting the moment
17.2 Evaluating the graphs
Problems
18 Mass renormalization
18.1 Vacuum expectation values
18.2 Electron self-energy
18.3 Pole mass
18.4 Minimal subtraction
18.5 Summary and discussion
Problems
19 Renormalized perturbation theory
19.1 Counterterms
19.2 Two-point functions
19.3 Three-point functions
19.4 Renormalization conditions in QED
19.5 Z1 = Z2: implications and proof
Problems
20 Infrared divergences
20.1 e+e− → μ+μ−(+γ)
20.2 Jets
20.3 Other loops
20.A Dimensional regularization
Problems
21 Renormalizability
21.1 Renormalizability of QED
21.2 Non-renormalizable field theories
Problems
22 Non-renormalizable theories
22.1 The Schrödinger equation
22.2 The 4-Fermi theory
22.3 Theory of mesons
22.4 Quantum gravity
22.5 Summary of non-renormalizable theories
22.6 Mass terms and naturalness
22.7 Super-renormalizable theories
Problems
23 The renormalization group
23.1 Running couplings
23.2 Renormalization group from counterterms
23.3 Renormalization group equation for the 4-Fermi theory
23.4 Renormalization group equation for general interactions
23.5 Scalar masses and renormalization group flows
23.6 Wilsonian renormalization group equation
Problems
24 Implications of unitarity
24.1 The optical theorem
24.2 Spectral decomposition
24.3 Polology
24.4 Locality
Problems
Part IV The Standard Model
25 Yang–Mills theory
25.1 Lie groups
25.2 Gauge invariance and Wilson lines
25.3 Conserved currents
25.4 Gluon propagator
25.5 Lattice gauge theories
Problems
26 Quantum Yang–Mills theory
26.1 Feynman rules
26.2 Attractive and repulsive potentials
26.3 e+e− → hadrons and αs
26.4 Vacuum polarization
26.5 Renormalization at 1-loop
26.6 Running coupling
26.7 Defining the charge
Problems
27 Gluon scattering and the spinor-helicity formalism
27.1 Spinor-helicity formalism
27.2 Gluon scattering amplitudes
27.3 gg → gg
27.4 Color ordering
27.5 Complex momenta
27.6 On-shell recursion
27.7 Outlook
Problems
28 Spontaneous symmetry breaking
28.1 Spontaneous breaking of discrete symmetries
28.2 Spontaneous breaking of continuous global symmetries
28.3 The Higgs mechanism
28.4 Quantization of spontaneously broken gauge theories
Problems
29 Weak interactions
29.1 Electroweak symmetry breaking
29.2 Unitarity and gauge boson scattering
29.3 Fermion sector
29.4 The 4-Fermi theory
29.5 CP violation
Problems
30 Anomalies
30.1 Pseudoscalars decaying to photons
30.2 Triangle diagrams with massless fermions
30.3 Chiral anomaly from the integral measure
30.4 Gauge anomalies in the Standard Model
30.5 Global anomalies in the Standard Model
30.6 Anomaly matching
Problems
31 Precision tests of the Standard Model
31.1 Electroweak precision tests
31.2 Custodial SU(2), ρ, S, T and U
31.3 Large logarithms in flavor physics
Problems
32 Quantum chromodynamics and the parton model
32.1 Electron–proton scattering
32.2 DGLAP equations
32.3 Parton showers
32.4 Factorization and the parton model from QCD
32.5 Lightcone coordinates
Problems
Part V Advanced topics
33 Effective actions and Schwinger proper time
33.1 Effective actions from matching
33.2 Effective actions from Schwinger proper time
33.3 Effective actions from Feynman path integrals
33.4 Euler–Heisenberg Lagrangian
33.5 Coupling to other currents
33.6 Semi-classical and non-relativistic limits
33.A Schwinger’s method
Problems
34 Background fields
34.1 1PI effective action
34.2 Background scalar fields
34.3 Background gauge fields
Problems
35 Heavy-quark physics
35.1 Heavy-meson decays
35.2 Heavy-quark effective theory
35.3 Loops in HQET
35.4 Power corrections
Problems
36 Jets and effective field theory
36.1 Event shapes
36.2 Power counting
36.3 Soft interactions
36.4 Collinear interactions
36.5 Soft-Collinear Effective Theory
36.6 Thrust in SCET
Problems
Appendices
Appendix A Conventions
A.1 Dimensional analysis
A.2 Signs
A.3 Feynman rules
A.4 Dirac algebra
Problems
Appendix B Regularization
B.1 Integration parameters
B.2 Wick rotations
B.3 Dimensional regularization
B.4 Other regularization schemes

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