Fields, by Warren Siegel; S. James Gates; Martin Rocek; Marcu
This is an 885 page book in Mathematics covering the following topics: (1) Symmetry. Relativistic quantum mechanics and classical field theory. Poincar´e group = special relativity. Enlarged spacetime symmetries: conformal and supersymmetry. Equations of motion and actions for particles and fields/wave functions. Internal symmetries: global (classifying particles), local (field interactions); (2) Quanta. Quantum aspects of field theory. Perturbation theory: expansions in loops, helicity, and internal symmetry. Although some have conjectured that nonperturbative approaches might solve renormalization difficulties found in perturbation, all evidence indicates these problems worsen instead in complete theory; and (3) Higher spin. General spins. Spin 2 must be included in any complete theory of nature. Higher spins are observed experimentally for bound states, but may be required also as fundamental fields.