We investigate the time propagation of tachyonic (superluminal) and tardyonic (subluminal, ordinary) massive wave packets on cosmic scales. A normalizable wave packet cannot be monochromatic in momentum space and thus acquires a positional uncertainty (or packet width) that increases with travel distance. We investigate the question of how this positional uncertainty affects the uncertainty in the detection time for cosmic radiation on Earth. In the ultrarelativistic limit, we find a unified result, δx(t)/c3=m2δpt/p03, where δx(t) is the positional uncertainty, m is the mass parameter, δp is the initial momentum spread of the wave function, and p0 is the central momentum of the wave packet, which, in the ultrarelativistic limit, is equal to its energy. This result is valid for tachyons and tardyons; its interpretation is being discussed.
We study the transformation of the dressed electron propagator and the general N -point functions under a change in the covariant gauge of internal photon propagators. We re-establish the well known Landau-Khalatnikov-Fradkin transformation for the propagator and generalise it to arbitrary correlation functions in configuration space, finding that it coincides with the analogous result for scalar fields. We comment on the consequences for perturbative application in momentum-space.
The worldline formalism shares with string theory the property that it allows one to write down master integrals that eectively combine the contributions of many Feynman diagrams. While at the one-loop level these diagrams dier only by the position of the external legs along a xed line or loop, at multiloop they generally involve dierent topologies. Here we summarize various eorts that have been made over the years to exploit this property in a computationally meaningful way. As a rst example, we show how to generalize the Landau-Khalatnikov-Fradkin formula for the non-perturbative gauge transformation of the fermion propagator in QED to the general 2n -point case by pure manipulations at the path-integral level. At the parameter-integral level, we show how to integrate out individual photons in the low-energy expansion, and then sketch a recently introduced general framework for the analytical evaluation of such worldline integrals involving a reduction to quantum mechanics on the circle and the relation between inverse derivatives and Bernoulli polynomials.Loops and Legs in Quantum Field Theory -LL2022,
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