A global version of Gunther's polysymplectic formalism using vertical projections

Abstract

I construct a global version of the local polysymplectic approach to covariant Hamiltonian field theory pioneered by C. Gunther. Beginning with the geometric framework of the theory, I specialize to vertical vector fields to construct the (poly)symplectic structures, derive Hamilton's field equations, and construct a more-or-less natural Poisson bracket. I then examine a few key examples to determine the nature of the necessary vertical projections and find that the theory provides the geometric analog of the canonical transformation approach to covariant Hamiltonian field theory advanced by Struckmeier and Redelbach. I conclude with a few remarks about possible applications of this framework to the geometric quantization of classical field theories.

arXiv comment25 pages

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Cited by in corpus (3)

• Obstacles to the quantization of general relativity using symplectic structures
• Cotangent bundle reduction and Routh reduction for polysymplectic manifolds
• Regularized polysymplectic geometry and first steps towards Floer theory for covariant field theories