2 research outputs found
Alternative symplectic structures for SO(3,1) and SO(4) four-dimensional BF theories
The most general action, quadratic in the B fields as well as in the
curvature F, having SO(3,1) or SO(4) as the internal gauge group for a
four-dimensional BF theory is presented and its symplectic geometry is
displayed. It is shown that the space of solutions to the equations of motion
for the BF theory can be endowed with symplectic structures alternative to the
usual one. The analysis also includes topological terms and cosmological
constant. The implications of this fact for gravity are briefly discussed.Comment: 13 pages, LaTeX file, no figure
Covariant description of parametrized nonrelativistic Hamiltonian systems
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.Comment: 15 pages, latex file. corrected typos, minor changes done to match
published versio