Dressed Dirac Propagator from a Locally Supersymmetric $\mathcal{N}=1$ Spinning Particle

Abstract

We study the Dirac propagator dressed by an arbitrary number $N$ of photons by means of a worldline approach, which makes use of a supersymmetric $\mathcal{N}=1$ spinning particle model on the line, coupled to an external Abelian vector field. We obtain a compact off-shell master formula for the tree level scattering amplitudes associated to the dressed Dirac propagator. In particular, unlike in other approaches, we express the particle fermionic degrees of freedom using a coherent state basis, and consider the gauging of the supersymmetry, which ultimately amounts to integrating over a worldline gravitino modulus, other than the usual worldline einbein modulus which corresponds to the Schwinger time integral. The path integral over the gravitino reproduces the numerator of the dressed Dirac propagator.

16 pages. Discussion improved, references added. Matches published version

References in corpus (3)

• Worldline Green Functions for Arbitrary Feynman Diagrams
• Quantum mechanical path integrals in the first quantised approach to quantum field theory
• Worldline master formulas for the dressed electron propagator, part 2: On-shell amplitudes

Cited by in corpus (6)

• Light bending from eikonal in worldline quantum field theory
• Asymptotic dynamics on the worldline for spinning particles
• Classical off-shell currents
• Worldline instantons for nonlinear Breit-Wheeler pair production and Compton scattering
• Worldline instantons for the momentum spectrum of Schwinger pair production in space-time dependent fields
• Non-perturbative gauge transformations of arbitrary fermion correlation functions in quantum electrodynamics