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An exact representation of the causal QED fermion Greens function, in an arbritrary external electromagnetic field, derived by Fried, Gabellini and McKellar, and which naturally allows for non-perturbative approximations, is here used to calculate non-perturbative approximations to the Greens function in the simple case of a constant external field. Schwingers famous exact result is obtained as the limit as the order of the approximation approaches infinity.
We find dispersion laws for the photon propagating in the presence of mutually orthogonal constant external electric and magnetic fields in the context of the $theta $-expanded noncommutative QED. We show that there is no birefringence to the first o
We revisit the calculation of the fermion self-energy in QED in the presence of a magnetic field. We show that, after carrying out the renormalization procedure and identifying the most general perturbative tensor structure for the modified fermion {
We report far-field approximations to the derivatives and integrals of the Greens function for the Ffowcs Williams and Hawkings equation in the frequency domain. The approximations are based on the far-field asymptotic of the Greens function. The det
We present a derivation of the Gribov equation for the gluon/photon Greens function D(q). Our derivation is based on the second derivative of the gauge-invariant quantity Tr ln D(q), which we interpret as the gauge-boson `self-loop. By considering th
We present the analytic evaluation of the two-loop corrections to the amplitude for the scattering of four fermions in Quantum Electrodynamics, $f^- + f^+ + F^- + F^+ to 0$, with $f$ and $F$ representing a massless and a massive lepton, respectively.