Diagrammatica: The Path to Feynman Diagrams, Vol. 4 Book

	Introduction	xi
1	Lorentz and Poincare Invariance	1
1.1	Lorentz Invariance	1
1.2	Structure of the Lorentz Group	7
1.3	Poincare Invariance	10
1.4	Maxwell Equations	10
1.5	Notations and Conventions	12
2	Relativistic Quantum Mechanics of Free Particles	15
2.1	Hilbert Space	15
2.2	Matrices in Hilbert Space	22
2.3	Fields	25
2.4	Structure of Hilbert Space	29
3	Interacting Fields	32
3.1	Physical System	32
3.2	Hilbert Space	33
3.3	Magnitude of Hilbert Space	34
3.4	U-matrix, S-matrix	35
3.5	Interpolating Fields	39
3.6	Feynman Rules	46
3.7	Feynman Propagator	54
3.8	Scattering Cross Section	55
3.9	Lifetime	60
3.10	Numerical Evaluation	62
3.11	Schrodinger Equation, Bound States	62
4	Particles with Spin	68
4.1	Representations of the Lorentz Group	68
4.2	The Dirac Equation	76
4.3	Fermion Fields	79
4.4	The E.M. Field	85
4.5	Quantum Electrodynamics	87
4.6	Charged Vector Boson Fields	91
4.7	Electron-Proton Scattering. The Rutherford Formula	92
5	Explorations	98
5.1	Scattering Cross Section for e[superscript +]e[superscript -] [right arrow] [mu superscript + mu superscript -]	98
5.2	Pion Decay. Two Body Phase Space. Cabibbo Angle	101
5.3	Vector Boson Decay	105
5.4	Muon Decay. Fiertz Transformation	108
5.5	Hyperon Leptonic Decay	117
5.6	Pion Decay and PCAC	124
5.7	Neutral Pion Decay and PCAC	131
6	Renormalization	137
6.1	Introduction	137
6.2	Loop Integrals	137
6.3	Self Energy	145
6.4	Power Counting	148
6.5	Quantum Electrodynamics	151
6.6	Renormalizable Theories	153
6.7	Radiative Corrections: Lamb Shift	154
6.8	Radiative Corrections: Top Correction to [rho]-Parameter	157
6.9	Neutral Pion Decay and the Anomaly	162
7	Massive and Massless Vector Fields	169
7.1	Subsidiary Condition Massive Vector Fields	169
7.2	Subsidiary Condition Massless Vector Fields	171
7.3	Photon Helicities	173
7.4	Propagator and Polarization Vectors of Massive Vector Particles	174
7.5	Photon Propagator	177
7.6	Left Handed Photons	180
8	Unitarity	183
8.1	U-matrix	183
8.2	Largest Time Equation	185
8.3	Cutting Equations	187
8.4	Unitarity and Cutting Equation	191
8.5	Unitarity: General Case	197
8.6	Kallen-Lehmann Representation, Dispersion Relation	200
8.7	Momenta in Propagators	204
9	Quantum Electrodynamics: Finally	207
9.1	Unitarity	207
9.2	Ward Identities	208
Appendix A	Complex Spaces, Matrices, CBH Equation	213
A.1	Basics	213
A.2	Differentiation of Matrices	217
A.3	Functions of Matrices	218
A.4	The CBH Equation	220
Appendix B	Traces	224
B.1	General	224
B.2	Multi-Dimensional [gamma]-Matrices	230
B.3	Frequently Used Equations	231
Appendix C	Dimensional Regularization	233
Appendix D	Summary: Combinatorial Factors	243
D.1	Summary	243
D.2	External Lines, Spin Sums, Propagators	245
D.3	Combinatorial Factors	247
Appendix E	Standard Model	249
E.1	Lagrangian	249
E.2	Feynman Rules	258
Appendix F	Metric and Conventions	273
F.1	General Considerations	273
F.2	Translation Examples	279
F.3	Translation Dictionary	281
	Index	282