We have investigated the nonrelativistic limit of gauge theories for possible applications to quantum chemistry. In particular, we are able to show that local gauge theory using U(1) algebras is isomorphic to a Smoluchowski operator with an imaginary drift, and a complex energy. These additional terms are shown to vanish when changing to imaginary time and analysing the diffusion equation with the Fourier Transform method. However, unlike relativistic theories, where time takes a coordinate - like role, in the nonrelativistic limit it becomes the usual parameter of Newtonian mechanics, and therefore a time dependent gauge theory is treated separately. We are able to show that a local time dependent gauge theory produces a novel Importance Sampling strategy for Diffusion Monte Carlo even in the spinless case.

Nonrelativistic gauge theories: How to impose symmetries requirements in diffusion Monte Carlo simulations

ACS Spring 2022

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