A New Look At The Path Integral Of Quantum Mechanics

2010/09/30 by Edward Witten, Witten, Edward · 1 voice · 5 citations
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th

paper · pdf · doi:10.48550/arxiv.1009.6032

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.

Cited by

• Functional Determinants for Constrained Path Integrals in Minisuperspace Jackiw-Teitelboim Gravity
• A Stochastic Approach to the Definition of the Path Integral Measure
• On the Complexified Spacetime Manifold Mapping of AdS to dS
• Schwinger-Dyson approximants
• Complex Saddles of Charged-AdS Gravitational partition function

Discussions

• I have some questions about Witten's paper on Brane Quantisation (arxiv.org/abs/1009.6032) In it, he makes several unstated topological assumptions that seem unwarranted. He states that the symplectic [bsky, 3 points, 2 comments]

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