A New Look At The Path Integral Of Quantum Mechanics
High Energy Physics - Theory
2010-10-01 v1
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.
Cite
@article{arxiv.1009.6032,
title = {A New Look At The Path Integral Of Quantum Mechanics},
author = {Edward Witten},
journal= {arXiv preprint arXiv:1009.6032},
year = {2010}
}
Comments
77 pp