Hamiltonian formalism with several variables and quantum field theory, PartI

Details Hamiltonian formalism with several variables and quantum field theory, PartI Hamiltonian formalism with several variables and quantum field theory, PartI

2000-04-17

arxiv.org/abs/math-ph/0004020v3

Physics

Mathematical Physics

minor modifications in the introduction and ref. added. (42 pages)

Scientific paper

We discuss in this paper the canonical structure of classical field theory in finite dimensions within the {\it{pataplectic}} hamiltonian formulation, where we put forward the role of Legendre correspondance. We define the Poisson $\mathfrak{p}$-brackets and $\mathfrak{\omega}$-brackets which are the analogues of the Poisson bracket on forms. We formulate the equations of motion of forms in terms of $\mathfrak{p}$-brackets and $\mathfrak{\omega}$-brackets with the $n$-form ${\cal H}\omega $. As illustration of our formalism we present two examples: the interacting scalar fields and conformal string theory.

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