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.
Publié le : 2000-04-17
Classification:
Mathematical Physics,
General Relativity and Quantum Cosmology,
High Energy Physics - Theory,
Mathematics - Dynamical Systems
@article{0004020,
author = {Helein, Frederic and Kouneiher, Joseph},
title = {Hamiltonian formalism with several variables and quantum field theory,
PartI},
journal = {arXiv},
volume = {2000},
number = {0},
year = {2000},
language = {en},
url = {http://dml.mathdoc.fr/item/0004020}
}
Helein, Frederic; Kouneiher, Joseph. Hamiltonian formalism with several variables and quantum field theory,
PartI. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0004020/