New Dirac Delta function based methods with applications to perturbative expansions in quantum field theory

摘要

We derive new all-purpose methods that involve the Dirac Delta distribution.Some of the new methods use derivatives in the argument of the Dirac Delta. Wehighlight potential avenues for applications to quantum field theory and wealso exhibit a connection to the problem of blurring/deblurring in signalprocessing. We find that blurring, which can be thought of as a result ofmulti-path evolution, is, in Euclidean quantum field theory without spontaneoussymmetry breaking, the strong coupling dual of the usual small couplingexpansion in terms of the sum over Feynman graphs.