Alternative symplectic structures for SO(3,1) and SO(4) four-dimensional BF theories

TL;DR

This paper explores alternative symplectic structures in four-dimensional BF theories with SO(3,1) and SO(4) gauge groups, analyzing their implications for gravity and including topological and cosmological terms.

Contribution

It introduces new symplectic structures for BF theories with SO(3,1) and SO(4), expanding the understanding of their solution spaces and potential gravitational applications.

Findings

Multiple symplectic structures are possible for BF theories.

The solution space admits alternative symplectic geometries.

Implications for gravitational theories are discussed.

Abstract

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.