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