Abstract
We study the retarded field sourced by a uniformly accelerated particle in a non-local scalar field theory. While the presence of non-locality regularizes the field at the location of the source, we also show that Lorentz-invariant non-local field theories are particularly sensitive to the somewhat unphysical assumption of uniform acceleration, leading to logarithmic divergences on the acceleration horizon. Analytic properties of the non-local retarded Green function indicate that the divergences can be removed by placing appropriate sources on the acceleration horizon in the asymptotic past.
Highlights
Locality is deeply woven into our notion of physics: from classical mechanics to general relativity and quantum field theory, locality has been an undergirding principle across disciplines
We proved that the presence of nonlocality regularizes the field at the location of the source, while— for large timelike and spacelike distances away from the hyperbolically accelerated source—approaching the expression for the retarded field found in the local theory, in accordance with DeWitt’s notion of asymptotic causality encountered in nonlocal theories
Using a pair of test sources on a null cone we proved analytically that such sources give rise to logarithmic divergences in this particular nonlocal theory
Summary
Locality is deeply woven into our notion of physics: from classical mechanics to general relativity and quantum field theory, locality has been an undergirding principle across disciplines. While Ginzburg has deemed the problem of the radiation of uniformly accelerated charges solved [40,41,42], the field is still active, focusing on the influence of gravitation [43], studying scalar theory [44], or extending the studies to de Sitter spacetime [45,46] These considerations have provided much insight on the causal structure of fields propagating in Minkowski spacetime, the spacetime properties of retarded Green functions, and have brought to light some unphysical consequences of. IV, we will summarize our findings and outline possible future research directions
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