A New Look At The Path Integral Of Quantum Mechanics

TL;DR

This paper explores the complexification of the Feynman path integral in quantum mechanics, linking it to branes in a two-dimensional A-model and establishing connections with Chern-Simons theory and N=4 super Yang-Mills theory.

Contribution

It introduces a novel interpretation of quantum mechanical path integrals via branes and A-models, and relates three-dimensional Chern-Simons theory to four-dimensional N=4 super Yang-Mills theory.

Findings

Integration cycles correspond to branes in the A-model.

Chern-Simons path integral relates to N=4 super Yang-Mills theory.

Provides a geometric framework for quantum mechanics and gauge theories.

Abstract

The Feynman path integral of ordinary quantum mechanics is complexified and it is shown that possible integration cycles for this complexified integral are associated with branes in a two-dimensional A-model. This provides a fairly direct explanation of the relationship of the A-model to quantum mechanics; such a relationship has been explored from several points of view in the last few years. These phenomena have an analog for Chern-Simons gauge theory in three dimensions: integration cycles in the path integral of this theory can be derived from N=4 super Yang-Mills theory in four dimensions. Hence, under certain conditions, a Chern-Simons path integral in three dimensions is equivalent to an N=4 path integral in four dimensions.