A groupoid approach to quantization
E Hawkins - 2008 - projecteuclid.org
Many interesting C∗-algebras can be viewed as quantizations of Poisson manifolds. I
propose that a Poisson manifold may be quantized by a twisted polarized convolution C∗ …
propose that a Poisson manifold may be quantized by a twisted polarized convolution C∗ …
A Groupoid Construction of Functional Integrals: Brownian Motion and Some TQFTs
J Lackman - arxiv preprint arxiv:2402.05866, 2024 - arxiv.org
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 …
we shift the emphasis in differential geometry from the tangent bundle onto the pair …
Geometric Quantization Without Polarizations
J Lackman - arxiv preprint arxiv:2405.01513, 2024 - arxiv.org
We expound upon our (polarization-free) definition of the quantization map in geometric
quantization, which is justified using the Poisson sigma model and pieces together most …
quantization, which is justified using the Poisson sigma model and pieces together most …
A Canonical Quantization of Poisson Manifolds: a 2-Groupoid Scheme
J Lackman - arxiv preprint arxiv:2404.03628, 2024 - arxiv.org
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 …
quantization map, and show that it relates geometric and deformation quantization: the …
A Formal Equivalence of Deformation Quantization and Geometric Quantization (of Higher Groupoids) and Non-Perturbative Sigma Models
J Lackman - arxiv preprint arxiv:2303.05494, 2023 - arxiv.org
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 …
we formally show that Kontsevich's star product can be obtained from the twisted convolution …
[BOOK][B] Formality theory: From poisson structures to deformation quantization
C Esposito - 2014 - books.google.com
This book is a survey of the theory of formal deformation quantization of Poisson manifolds,
in the formalism developed by Kontsevich. It is intended as an educational introduction for …
in the formalism developed by Kontsevich. It is intended as an educational introduction for …
A Derivation of Geometric Quantization via Feynman's Path Integral on Phase Space
J Lackman - arxiv preprint arxiv:2405.17273, 2024 - arxiv.org
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 …
Kostant-Souriau and Weinstein, from Feynman's path integral formulation on phase space …
Generalized Kaehler geometry from supersymmetric sigma models
A Bredthauer, U Lindström, J Persson… - Letters in Mathematical …, 2006 - Springer
We give a physical derivation of generalized Kähler geometry. Starting from a
supersymmetric nonlinear sigma model, we rederive and explain the results of Gualtieri …
supersymmetric nonlinear sigma model, we rederive and explain the results of Gualtieri …
On an Axiomatization of Path Integral Quantization and its Equivalence to Berezin's Quantization
J Lackman - arxiv preprint arxiv:2410.02739, 2024 - arxiv.org
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 …
integral formulation of quantization is equivalent to an abstract operator formulation, ie …
Six lectures on geometric quantization
K Wernli - arxiv preprint arxiv:2306.00178, 2023 - arxiv.org
Six lectures on Geometric Quantization arxiv:2306.00178v1 [math-ph] 31 May 2023 Page 1 Six
lectures on Geometric Quantization Konstantin Wernli June 2, 2023 Abstract These are the …
lectures on Geometric Quantization Konstantin Wernli June 2, 2023 Abstract These are the …