Hamiltonian formalism with several variables and quantum field theory, PartI

2000/04/17 by Frédéric Hélein, Frederic Helein, Helein, Frederic +2 · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Numerical methods for differential equations #gr-qc #hep-th #math-ph #math.DS #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/0004020

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

openalex publication_date 2000/04/17 · arxiv created 2000/04/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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