Dressed Dirac propagator from a locally supersymmetric N=1 spinning particle

Corradini , Olindo; Esposti, Gianluca Degli

doi:10.1016/j.nuclphysb.2021.115498

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Dressed Dirac propagator from a locally supersymmetric N=1 spinning particle

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Corradini , Olindo
AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Corradini, O., & Esposti, G. D. (2021). Dressed Dirac propagator from a locally supersymmetric N=1 spinning particle. Nuclear Physics B, 970: 115498. doi:10.1016/j.nuclphysb.2021.115498.

Cite as: https://hdl.handle.net/21.11116/0000-0006-F2C9-6

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 ${\cal N}
= 1$ 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.