N.S.B. Cosmic Center

Introduction: Perturbative solutions to nonlinear field equations. The prequantum effective action and S-matrix amplitudes. Some virtues of the effective action functional approach. Conventions and bibliographic remarks.

Scalar and Vector Fields: Perturbative real scalar with a quartic self-coupling. The prequantum effective action. Momentum space expressions and Feynman graphs. The free field and the Hamiltonian. S-matrix rules. Amplitudes for scattering, decay and particle production. Complex scalars, antiparticles, charge conservation, and crossing symmetry. Vector fields. Instructive problems.

Spinor Fields: Free Dirac fields. Orthonormalization and completeness relations. Hamiltonian and charge. S-matrix rules. Massless spinors. Instructive problems.

Yukawa Coupling Theories: Perturbative scalars and spinors in a simple Yukawa system. The prequatum effective action. Nucleons and pions. Nucleon-pion prequantum effective action. Instructive problems.

Prequantum Electrodynamics: Perturbative electron and photon fields. The prequantum effective electrodynamic action. Compton scattering. Pair annihilation. Electron-electron scattering. Electron-positron scattering. Instructive problems.

Non-Commutative Gauge Theory: Perturbative quarks and gluons. Prequantum effective chromodynamics. Instructive problems.

Supersymmetric Theory: Perturbative superfield solutions. The prequantum effective superfield action. Instructive problems.

Supersymmetric Gauge Theory: Perturbative matter and gauge superfields. The prequantum effective superchromodynamic action. Instructive problems.

Appendix: Spin-2 free fields. Spin-3/2 free fields. Perturbative formulae. Superfield formulae.