Covariant description of parametrized nonrelativistic Hamiltonian systems

Abstract

The various phase spaces involved in the dynamics of parametrized nonrelativistic Hamiltonian systems are displayed by using Crnkovic and Witten's covariant canonical formalism. It is also pointed out that in Dirac's canonical formalism there exists a freedom in the choice of the symplectic structure on the extended phase space and in the choice of the equations that define the constraint surface with the only restriction that these two choices combine in such a way that any pair (of these two choices) generates the same gauge transformation. The consequence of this freedom on the algebra of observables is also discussed.

arXiv comment15 pages, latex file. corrected typos, minor changes done to match published version

References in corpus (2)

• The century of the incomplete revolution: searching for general relativistic quantum field theory
• Relational evolution of the degrees of freedom of generally covariant quantum theories

Cited by in corpus (5)

• Covariant canonical formalism for four-dimensional BF theory
• Alternative symplectic structures for SO(3,1) and SO(4) four-dimensional BF theories
• Symplectic quantization, inequivalent quantum theories, and Heisenberg's principle of uncertainty
• Hamilton-Jacobi theory for Hamiltonian systems with non-canonical symplectic structures
• Genuine covariant description of Hamiltonian dynamics