4 papers
A Mathematical Definition of Path Integrals on Symplectic Manifolds
Joshua Lackman
We give a mathematical definition of some path integrals, emphasizing those relevant to the quantization of symplectic manifolds (and more generally, Poisson manifolds) $\unicode{x…
A Canonical Quantization of Poisson Manifolds: a 2-Groupoid Scheme
Joshua Lackman
We canonically quantize a Poisson manifold to a Lie 2-groupoid, complete with a quantization map, and show that it relates geometric and deformation quantization: the perturbative…
A Groupoid Construction of Functional Integrals: Brownian Motion and Some TQFTs
Joshua Lackman
We formalize Feynman's construction of the quantum mechanical path integral. To do this, we shift the emphasis in differential geometry from the tangent bundle onto the pair groupo…
A Formal Equivalence of Deformation Quantization and Geometric Quantization (of Higher Groupoids) and Non-Perturbative Sigma Models
Joshua Lackman
Based on work done by Bonechi, Cattaneo, Felder and Zabzine on Poisson sigma models, we formally show that Kontsevich's star product can be obtained from the twisted convolution al…