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arXiv · 1009.6032

A New Look At The Path Integral Of Quantum Mechanics

Edward Witten
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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.

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Edward Witten. 2010-09-30. A New Look At The Path Integral Of Quantum Mechanics. https://arxiv.org/abs/1009.6032

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