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One-particle reducible contribution to the one-loop spinor propagator in a constant field
Ahmadiniaz, N.,Bastianelli, F.,Corradini, O.,Edwards, J.P.,Schubert, C. North Holland 2017 Nuclear physics, B Vol.924 No.-
Extending work by Gies and Karbstein on the Euler-Heisenberg Lagrangian, it has recently been shown that the one-loop propagator of a charged scalar particle in a constant electromagnetic field has a one-particle reducible contribution in addition to the well-studied irreducible one. Here we further generalize this result to the spinor case, and find the same relation between the reducible term, the tree-level propagator and the one-loop Euler-Heisenberg Lagrangian as in the scalar case. Our demonstration uses a novel worldline path integral representation of the photon-dressed spinor propagator in a constant electromagnetic field background.
Multiphoton amplitudes and generalized Landau-Khalatnikov-Fradkin transformation in scalar QED
Ahmadiniaz, Naser,Bashir, Adnan,Schubert, Christian American Physical Society 2016 Physical Review D Vol.93 No.4
<P>We apply the worldline formalism to amplitudes in scalar quantum electrodynamics involving open scalar lines, with an emphasis on their nonperturbative gauge dependence. At the tree level, we study the scalar propagator interacting with any number of photons in configuration space as well as in momentum space. At one loop we rederive, in an efficient way, the off-shell vertex in an arbitrary dimension and any covariant gauge. Generalizing the Landau-Khalatnikov-Fradkin transformation for the nonperturbative propagator, we find simple nonperturbative transformation rules for arbitrary x-space amplitudes under a change of the covariant gauge parameter in terms of conformal cross ratios.</P>
Master formulas for the dressed scalar propagator in a constant field
Ahmad, A.,Ahmadiniaz, N.,Corradini, O.,Kim, S.P.,Schubert, C. North Holland 2017 Nuclear Physics, Section B Vol.919 No.-
The worldline formalism has previously been used for deriving compact master formulas for the one-loop N-photon amplitudes in both scalar and spinor QED, and in the vacuum as well as in a constant external field. For scalar QED, there is also an analogous master formula for the propagator dressed with N photons in the vacuum. Here, we extend this master formula to include a constant field. The two-photon case is worked out explicitly, yielding an integral representation for the Compton scattering cross section in the field suitable for numerical integration in the full range of electric and magnetic field strengths.