5 papers
Isometric Embeddings and Hyperkähler Geometry of the Cotangent Bundle of Complex Projective Space via the Scheme of Rank-1 Projections
Joshua Lackman
We show that the hyperkahler geometry of can be described algebraically by the affine scheme of rank-1 projections, and that this description simultaneously…
A Geometric Definition of the Integral and Applications
Joshua Lackman
The standard definition of integration of differential forms is based on local coordinates and partitions of unity. This definition is mostly a formality and not used used in expli…
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…