Geometric (pre)quantization in the polysymplectic approach to field theory

2001/12/31 by I. V. Kanatchikov, Kanatchikov, I. V. · 1 citation
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Symplectic Geometry (math.SG) #hep-th #math-ph #math.MP #math.SG #quant-ph

paper · pdf · doi:10.48550/arxiv.hep-th/0112263

12 pages, LaTeX. V2: minor corrections, important Note added in proofs, references detailed

arxiv created 2002/06/03 · arxiv updated 2009/11/30

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.

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• Modifications of Newtonian dynamics from higher moments of quantum spin connection in precanonical quantum gravity

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