Quantum Field Theory: From Operators to Path Integrals

QFT: Operators to Path Integrals......Page p0003.djvu
2010 ISBN 978-3-527-40846-7......Page p0004.djvu
Contents......Page p0007.djvu
Preface......Page p0013.djvu
1.1 The Classical String......Page p1.djvu
1.3 The Quantum String......Page p5.djvu
1.4 Second Quantization......Page p6.djvu
1.5 Creation and Annihilation Operators......Page p9.djvu
1.6 Bose and Fermi Statistics......Page p11.djvu
2.1 K1ein—Gordon Equation......Page p17.djvu
2.2 Real Scalar Field......Page p18.djvu
2.3 Energy and Momentum......Page p19.djvu
2.4 Particle Spectrum......Page p21.djvu
2.5 Continuum Normalization......Page p22.djvu
2.6 Complex Scalar Field......Page p23.djvu
2.7 Charge and Antiparticle......Page p25.djvu
2.8 Microcausality......Page p26.djvu
2.9 The Feynman Propagator......Page p27.djvu
2.10 The Wave Functional......Page p29.djvu
2.11 Functional Operations......Page p30.djvu
2.12 Vacuum Wave Functional......Page p32.djvu
2.13 The Phi^4 Theory......Page p34.djvu
3.1 Lorentz Transformations......Page p39.djvu
3.2 Minimal Representation: SL(2C)......Page p41.djvu
3.3 The Poincaré Group......Page p43.djvu
3.4 Scalar, Vector, and Spinor Fields......Page p45.djvu
3.5 Relativistic Quantum Fields......Page p47.djvu
3.6 One-Particle States......Page p48.djvu
4.1 Principle of Stationary Action......Page p55.djvu
4.2 Noether’s Theorem......Page p57.djvu
4.3 Translational Invariance......Page p58.djvu
4.4 Lorentz Invariance......Page p61.djvu
4.5 Symmetrized Energy-Momentum Tensor......Page p63.djvu
4.6 Gauge Invariance......Page p65.djvu
5.1 Maxwell’s Equations......Page p69.djvu
5.2 Covariance of the Classical Theory......Page p71.djvu
5.3 Canonical Formalism......Page p73.djvu
5.4 Quantization in Coulomb Gauge......Page p75.djvu
5.5 Spin Angular Momentum......Page p78.djvu
5.6 Intrinsic Parity......Page p79.djvu
5.7 Transverse Propagator......Page p81.djvu
5.8 Vacuum Fluctuations......Page p82.djvu
5.9 The Casimir Effect......Page p84.djvu
5.10 The Gauge Principle......Page p88.djvu
6.1 Dirac Algebra......Page p95.djvu
6.2 Wave Functions and Current Density......Page p98.djvu
6.3 Plane Waves......Page p99.djvu
6.4 Lorentz Transformations......Page p102.djvu
6.5 Interpretation of Dirac Matrices......Page p105.djvu
6.6 External Electromagnetic Field......Page p106.djvu
6.7 Non-Relativistic Limit......Page p108.djvu
6.8 Thomas Precession......Page p110.djvu
6.9 Hole Theory......Page p112.djvu
6.10 Charge Conjugation......Page p115.djvu
6.11 Massless Particles......Page p116.djvu
7.1 Quantization of the Dirac Field......Page p123.djvu
7.2 Feynman Propagator......Page p126.djvu
7.4 Electromagnetic Interactions......Page p128.djvu
7.5 Isospin......Page p129.djvu
7.6 Parity......Page p131.djvu
7.7 Charge Conjugation......Page p132.djvu
7.8 Time Reversal......Page p133.djvu
8.1 Time Evolution......Page p139.djvu
8.2 Interaction Picture......Page p140.djvu
8.3 Adiabatic Switching......Page p142.djvu
8.4 Correltn. Fns in the Interaction Picture......Page p145.djvu
8.5 S—Matrix and Scattering......Page p147.djvu
8.6 Scattering Cross Section......Page p148.djvu
8.7 Potential Scattering......Page p151.djvu
8.8 Adiabatic Theorem......Page p154.djvu
9.1 Perturbation Theory......Page p159.djvu
9.2 Time-Ordered & Normal Products......Page p160.djvu
9.3 Wick’s Theorem......Page p161.djvu
9.4 Feynman Rules for Scalar Theory......Page p164.djvu
9.5.1 Vacuum Graph......Page p169.djvu
9.5.3 Connected Graph......Page p170.djvu
9.6 Wick Rotation......Page p171.djvu
9.7 Regularization Schemes......Page p172.djvu
9.8 Linked-Cluster Theorem......Page p173.djvu
9.9 Vacuum Graphs......Page p174.djvu
10.1 Feynman Rules......Page p181.djvu
10.2 Reduction Formula......Page p184.djvu
10.3 The Generating Functional......Page p187.djvu
10.4 Connected Correlation Functions......Page p188.djvu
10.5 Lehmann Representation......Page p189.djvu
10.6 Dyson—Schwinger Equations......Page p192.djvu
10.7 Bound States......Page p195.djvu
10.8 Bethe—Salpeter Equation......Page p198.djvu
11.1 Interaction Hamiltonian......Page p203.djvu
11.2 Photon Propagator......Page p205.djvu
11.3 Feynman Graphs......Page p209.djvu
11.4 Feynman Rules......Page p214.djvu
11.5 Properties of Feynman Graphs......Page p215.djvu
12.1 Compton Scattering......Page p219.djvu
12.2 Electromagnetic Form Factors......Page p223.djvu
12.3 Anomalous Magnetic Moment......Page p227.djvu
12.4 Charge Distribution......Page p230.djvu
13.1 Primitive Divergences in QED......Page p235.djvu
13.2 Electron Self-Energy......Page p237.djvu
13.3 Vacuum Polarization......Page p241.djvu
13.4 Running Coupling Constant......Page p244.djvu
13.5 Full Vertex......Page p245.djvu
13.6 Ward Identity......Page p246.djvu
13.7 Renormalization to 2nd Order......Page p248.djvu
13.8 Renormalization to All Orders......Page p249.djvu
13.9 Callan—Symanzik Equation......Page p253.djvu
13.10 Triviality......Page p255.djvu
14.1 Path integrals in Quantum Mechanics......Page p261.djvu
14.2 Time-ordering......Page p264.djvu
14.3 Imaginary Time......Page p265.djvu
14.4 Path Integrals in Quantum Field Theory......Page p266.djvu
14.5 Euclidean Space—time......Page p267.djvu
14.6 Vacuum Amplitudes......Page p268.djvu
14.7 Statistical Mechanics......Page p271.djvu
14.8 Gaussian Integrals......Page p273.djvu
14.9 Perturbation Theory......Page p276.djvu
14.10 The Loop Expansion......Page p279.djvu
14.11 Boson and Fermion Loops......Page p280.djvu
14.12 Grassmann Variables......Page p282.djvu
15.1 Why Broken Symmetry......Page p291.djvu
15.2 Ferromagnetism......Page p294.djvu
15.3 Spin Waves......Page p296.djvu
15.4 Breaking Gauge Invariance......Page p299.djvu
15.5 Superfluidity......Page p302.djvu
15.6 Ginsburg—Landau Theory......Page p305.djvu
15.7 Effective Action......Page p307.djvu
15.8 Effective Potential......Page p308.djvu
16.1 The Cutoff as Scale Parameter......Page p315.djvu
16.2 RG Trajectories......Page p318.djvu
16.3 Fixed points......Page p319.djvu
16.4 Momentum Space RG......Page p320.djvu
16.5 Real Space RG......Page p322.djvu
16.6 Renormalization of Correlation Functions......Page p325.djvu
16.7 Relevant and Irrelevant Parameters......Page p326.djvu
16.8 The Free Field......Page p327.djvu
16.9 IR Fixed Point and Phase Transition......Page p329.djvu
16.10 Crossover......Page p330.djvu
16.11 Perturbative Renormalization Revisited......Page p331.djvu
16.12 Critical Evaluation......Page p332.djvu
16.13 Why Correct Theories Are Beautiful......Page p333.djvu
17.1 Stability ofthe Free Field......Page p339.djvu
17.2 General Scalar Field......Page p340.djvu
17.3 Feynman Graphs......Page p341.djvu
17.4 Wegner—Houghton Equation......Page p343.djvu
17.5 Renormalized Couplings......Page p346.djvu
17.6 The RG Matrix......Page p348.djvu
17.7 Non-Triviality and Asymptotic Freedom......Page p351.djvu
17.8 The Case d = 2......Page p353.djvu
18.1 Absence of Long-Range Order......Page p357.djvu
18.2 Topological Order......Page p358.djvu
18.3 XY Model......Page p360.djvu
18.5 Vortex Model......Page p364.djvu
18.6 Two-D Superfluidity......Page p366.djvu
18.7 RG Trajectories......Page p368.djvu
18.8 Universal Jump of Superfluid Density......Page p372.djvu
19.1 Topological Soliton......Page p375.djvu
19.2 Instanton and Tunneling......Page p378.djvu
19.3 Depinning of Charge Density Waves......Page p379.djvu
19.4 Nonlinear Sigma Model......Page p383.djvu
19.5 The Skyrmion......Page p385.djvu
19.6 The Hopf Invariant......Page p389.djvu
19.7 Fractional Spin......Page p391.djvu
19.8 Monopoles, Vortices, and Anomalies......Page p393.djvu
A.1 Notation......Page p399.djvu
A.2 Classical Mechanics......Page p400.djvu
A.3 Quantum Mechanics......Page p401.djvu
B.1 Linear Response......Page p405.djvu
B.2 Normal Fluid and Superfluid......Page p406.djvu
B.3 Superfluid Density......Page p408.djvu
C.1 Renormalization Scheme......Page p411.djvu
C.2 The Equation......Page p412.djvu
C.3 Asymptotically Free Scalar Field......Page p414.djvu
Index......Page p417.djvu