Propagators and Path Integrals

Path-integral expressions for one-particle propagators in scalar and fermionic field theories are derived, for arbitrary mass. This establishes a direct connection between field theory and specific classical point-particle models. The role of world-line reparametrization invariance of the classical action and the implementation of the corresponding BRST-symmetry in the quantum theory are discussed. The presence of classical worldline supersymmetry is shown to lead to an unwanted doubling of states for massive spin-1/2 particles. The origin of this phenomenon is traced to a ‘hidden’ topological fermionic excitation. A different formulation of the pseudo-classical mechanics using a bosonic representation of γ5 is shown to remove these extra states at the expense of losing manifest supersymmetry.