this book provides an easily accessible introduction to quantum field theory via feynman rules and calculations in particle physics.the aim is to make clear what the physical foundations of present day field theory are, to clarify the physical content of feynman rules, and to outline their domain of applicability. the book begins with a brief review of some aspects of einstein's theory of relativity that are of particular importance for field theory,before going on to consider the relativistic quantum mechan-ics of free particles, interacting fields, and particles with spin.the techniques learnt in these chapters are then demonstrated in examples that might be encountered in real accelerator physics.further chapters contain discussions on renormalization, massive and massless vector fields and unitarity. a final chapter presents concluding arguments concerning quantum electrodynamics. the book includes valuable appendices that review some essential mathematics, including complex spaces, matrices, the cbh equa-tion, traces and dimensional regularization. an appendix contain-ing a comprehensive summary of the rules and conventions used is followed by an appendix specifying the full langranian of the standard model and the corresponding feynman rules. to make the book useful for a wide audience a final appendix provides a discussion on the metric used, and an easy-to-use dictionary con-necting equations written with a different metric. written as a textbook, many diagrams and examples are included.
this book will be used by beginning graduate students taking courses in particle physics or quantum field theory, as well as by researchers as a source and reference book on feynman diagrams and rules.
introduction
1 lorentz and poincare invariance
1.1 lorentz invariance
1.2 structure of the lorentz group
1.3 poincare invariance
1.4 maxwell equations
1.5 notations and conventions
2 relativistic quantum mechanics of free particles
2.1 hilbert space
2.2 matrices in hilbert space
2.3 fields
2.4 structure of hilbert space
3 interacting fields
3.1 physical system
3.2 hilbert space
introduction
1 lorentz and poincare invariance
1.1 lorentz invariance
1.2 structure of the lorentz group
1.3 poincare invariance
1.4 maxwell equations
1.5 notations and conventions
2 relativistic quantum mechanics of free particles
2.1 hilbert space
2.2 matrices in hilbert space
2.3 fields
2.4 structure of hilbert space
3 interacting fields
3.1 physical system
3.2 hilbert space
3.3 magnitude of hilbert space
3.4 u-matrix, s-matrix
3.5 interpolating fields
3.6 feynman rules
3.7 feynman propagator
3.8 scattering cross section
3.9 lifetime
3.10 numerical evaluation
3.11 schrodinger equation, bound states
4 particles with spin
4.1 representations of the lorentz group
4.2 the dirac equation
4.3 fermion fields
4.4 the e.m. field
4.5 quantum electrodynamics
4.6 charged vector boson fields
4.7 electron-proton scattering. the rutherford formula
5 explorations
5.1 scattering cross section for e+e-→μ+μ-
5.2 pion decay. two body phase space. cabibbo angle
5.3 vector boson decay
5.4 muon decay. fiertz transformation
5.5 hyperon leptonic decay
5.6 pion decay and pcac
5.7 neutral pion decay and pcac
6 renormalization
6.1 introduction
6.2 loop integrals
6.3 self energy
6.4 power counting
6.5 quantum electrodynamics
6.6 renormalizable theories
6.7 radiative corrections: lamb shift
6.8 radiative corrections: top correction to p-parameter
6.9 neutral pion decay and the anomaly
7 massive and massless vector fields
7.1 subsidiary condition massive vector fields
7.2 subsidiary condition massless vector fields
7.3 photon helicities
7.4 propagator and polarization vectors of massive vector particles
7.5 photon propagator
7.6 left handed photons
8 unitarity
8.1 u-matrix
8.2 largest time equation
8.3 cutting equations
8.4 unitarity and cutting equation
8.5 unitarity: general case
8.6 kallen-lehmann representation, dispersion relation
8.7 momenta in propagators
9 quantum electrodynamics: finally
9.1 unitarity
9.2 ward identities
appendix a complex spaces, matrices, cbh equatioh
a.1 basics
a.2 differentiation of matrices
a.3 functions of matrices
a.4 the cbh equation
appendix b traces
b. 1 general
b.2 multi-dimensional y-matrices
b.3 frequently used equations
appendix c dimensional regularization
appendix d summary. combinatorial factors
d.1 summary
d.2 external lines, spin sums, propagators
d.3 combinatorial factors
appendix e standard model
e. 1 lagrangian
e.2 feynman rules
appendix f metric and conventions
f.1 general considerations
f.2 translation examples
f.3 translation dictionary
index
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