A new look at the path integral of quantum mechanics

By E. Witten. 2010

211 citations recorded by the source corpus.

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.

Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f1e23f843147ef9f21f3d676ce6743025be42b4e

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Citations in the corpus

Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles (2014, methodology): “path integral is regularized into a nite dimensional integral35, and the connection of resurgence theory to the Lefshetz thimble decompositions of integration cycles (which was explained in detail in [52,99]) becomes particularly clear. Let the two dimensional lattice have L 1L 2 sites. Then the ori”
Fivebranes and Knots (2011, methodology): “We are actually now in a situation that has been analyzed in detail in section 5 of [45].”
Chern-Simons theory and S-duality (2011, background): “ LGsuggests that this hidden symmetry should have a physical explanation in the construction of Chern-Simons Hilbert spaces and wavefunctions in terms of four-dimensional N= 4 super-Yang-Mills theory [12, 13, 3] or, equivalently, in terms of six-dimensional (2;0) theory compactied on a torus. By und”
Knot Invariants from Four-Dimensional Gauge Theory (2011, background): “For an explanation of this from a physical point of view (in the context of supersymmetric quantum mechanics related to Morse theory), see [43] or [41].”
Quantum Riemann Surfaces in Chern-Simons Theory (2011, methodology): “eger; so if k2Z the path integral (2.5) is well-dened. If Gis not compact, this quantization of the level is not always necessary [30, 31]. As proposed in [1], and further discussed and developed in [2, 3, 21], the level kor its inverse ~ can be analytically continued to arbitrary nonzero complex nu”
A primer on resurgent transseries and their asymptotics (2018, unknown): “, [234, 235, 142, 61, 223, 222, 160, 31, 224, 30, 125, 104, 225], and lattice field theory, e.”