9,623 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
Concordance of actions on
We consider locally linear Z_p x Z_p actions on the four-sphere. We present
simple constructions of interesting examples, and then prove that a given
action is concordant to its linear model if and only if a single surgery
obstruction taking to form of an Arf invariant vanishes. We discuss the
behavior of this invariant under various connected-sum operations, and conclude
with a brief discussion of the existence of actions which are not concordant to
their linear models
Equivalent and Alternative Forms for BF Gravity with Immirzi Parameter
A detailed analysis of the BF formulation for general relativity given by
Capovilla, Montesinos, Prieto, and Rojas is performed. The action principle of
this formulation is written in an equivalent form by doing a transformation of
the fields of which the action depends functionally on. The transformed action
principle involves two BF terms and the two Lorentz invariants that appear in
the original action principle generically. As an application of this formalism,
the action principle used by Engle, Pereira, and Rovelli in their spin foam
model for gravity is recovered and the coupling of the cosmological constant in
such a formulation is obtained
- …