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A Simple Description of the Hyperkähler Structure of the Cotangent Bundle of Projective Space via Quantization
Joshua Lackman
Quantization identifies the cotangent bundle of projective space with the (non-Hermitian) rank- projections of a Hilbert space. We use this identification to study the natural g…
Quantization of Holomorphic Symplectic Manifolds: Analytic Continuation of Path Integrals and Coherent States
Joshua Lackman
We extend Berezin's quantization to holomorphic symplectic manifolds, which involves replacing the state space with its comple…
On an Axiomatization of Path Integral Quantization and its Equivalence to Berezin's Quantization
Joshua Lackman
We axiomatize path integral quantization of symplectic manifolds. We prove that this path integral formulation of quantization is equivalent to an abstract operator formulation, ie…
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 Derivation of Geometric Quantization via Feynman's Path Integral on Phase Space
Joshua Lackman
We derive the geometric quantization program of symplectic manifolds, in the sense of both Kostant-Souriau and Weinstein, from Feynman's path integral formulation on phase space. T…
Geometric Quantization Without Polarizations
Joshua Lackman
We derive the quantization map in geometric quantization of symplectic manifolds via the Poisson sigma model. This gives a polarization-free (path integral) definition of quantizat…
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…