A New Look At The Path Integral Of Quantum Mechanics

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.

77 pp

References in corpus (10)

• Phases of $N=2$ Theories In Two Dimensions
• Vortex Counting and Lagrangian 3-manifolds
• Khovanov-Rozansky Homology and Topological Strings
• Remarks on A-branes, Mirror Symmetry, and the Fukaya category
• The Witten equation and its virtual fundamental cycle
• A-twisted Landau-Ginzburg models
• Instantons beyond topological theory II
• The Witten equation, mirror symmetry and quantum singularity theory
• Coisotropic Branes, Noncommutativity, and the Mirror Correspondence
• Mirror symmetry and deformation quantization

Cited by in corpus (30)

• An Introduction to Resurgence, Trans-Series and Alien Calculus
• Branes And Supergroups
• Lefschetz-thimble analysis of the sign problem in one-site fermion model
• Structure of Lefschetz thimbles in simple fermionic systems
• Lefschetz thimble structure in one-dimensional lattice Thirring model at finite density
• Toward Picard-Lefschetz Theory of Path Integrals, Complex Saddles and Resurgence
• Lefschetz thimbles and stochastic quantisation: Complex actions in the complex plane
• Evading the sign problem in the mean-field approximation through Lefschetz-thimble path integral
• Lefschetz-thimble techniques for path integral of zero-dimensional $O(n)$ sigma models
• Functional methods for false vacuum decay in real time
• Hamilton dynamics for the Lefschetz thimble integration akin to the complex Langevin method
• Holographic Complex Conformal Field Theories
• Teichmuller TQFT vs Chern-Simons Theory
• Biadjoint scalar tree amplitudes and intersecting dual associahedra
• Ω-deformation of B-twisted gauge theories and the 3d-3d correspondence
• What is QFT? Resurgent trans-series, Lefschetz thimbles, and new exact saddles
• Boundary conditions for GL-twisted N=4 SYM
• Wormholes in Quantum Mechanics
• Quantization via Mirror Symmetry
• Condensates and instanton - torus knot duality. Hidden Physics at UV scale
• Why Is Landau-Ginzburg Link Cohomology Equivalent To Khovanov Homology?
• The Response Field and the Saddle Points of Quantum Mechanical Path Integrals
• Geodesics on Calabi-Yau manifolds and winding states in nonlinear sigma models
• Lorentzian quantum cosmology in novel Gauss-Bonnet gravity from Picard-Lefschetz methods
• Lefschetz Thimbles and Quantum Phases in Zero-Dimensional Bosonic Models
• A String Dual for Partially Topological Chern-Simons-Matter Theories
• Semi-Classical Analysis of the String Theory Cigar
• Simulating low dimensional QCD with Lefschetz thimbles
• Non-commutative Toric Varieties
• Non-perturbative Aspects of Quantum Field Theories from Holography