Geometric (pre)quantization in the polysymplectic approach to field theory
arXiv:hep-th/0112263
Abstract
The prequantization map for a Poisson-Gerstenhaber algebra of dynamical variables represented by differential forms within the polysymplectic formulation of the De Donder--Weyl covariant Hamiltonian field theory is presented and the corresponding prequantum Schroedinger equation for a non-homogeneous form valued wave function is derived. This is the first step toward understanding the procedures of covariant precanonical field quantization from the point of view of geometric quantization.
12 pages, LaTeX. V2: minor corrections, important Note added in proofs, references detailed
References in corpus (11)
- Geometry of multisymplectic Hamiltonian first-order field theories
- On Field Theoretic Generalizations of a Poisson Algebra
- De Donder-Weyl Equations and Multisymplectic Geometry
- DeDonder-Weyl theory and a hypercomplex extension of quantum mechanics to field theory
- Finite dimesional Hamiltonian formalism for gauge and field theories
- A Poisson Bracket on Multisymplectic Phase Space
- On the Multimomentum Bundles and the Legendre Maps in Field Theories
- Novel algebraic structures from the polysymplectic form in field theory
- Covariant Geometric Prequantization of Fields
- From the Poincaré-Cartan form to a Gerstenhaber algebra of Poisson brackets in field theory
- Subquantum Models: Basic Principles, Effects and Tests
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- A review on geometric formulations for classical field theory: the Bonzom-Livine model for gravity
- Poly-Poisson Sigma models and their relational poly-symplectic groupoids
- Schrödinger Functional of a Quantum Scalar Field in Static Space-Times from Precanonical Quantization
- Precanonical structure of the Schrödinger wave functional in curved space-time
- Covariant Quantum Gravity I: Covariant Hamiltonian Framework