Spin current in BF theory

Abstract

In this paper, we introduce a current which we call spin current corresponding to the variation of the matter action in BF theory with respect to the spin connection $A$ which takes values in Lie algebra $\mathfrak{so}(3,\mathbb{C})$ in self-dual formalism. For keeping the constraint $D{B}^i=0$ satisfied, we suggest adding a new term to the BF Lagrangian using a new field ${\psi }^i$ which can be used for calculating the spin current. We derive the equations of motion and discuss the solutions. We will see that the solutions of that equations do not require a specific metric on the manifold $M$, we just need to know the symmetry of the system and the information about the spin current. Finally we find the solutions in a spherical and cylindrical symmetric systems.

arXiv comment23 pages, accepted for publication on Physics

References in corpus (11)

• An invitation to loop quantum gravity
• Currents and the Energy-Momentum Tensor in Classical Field Theory: A fresh look at an Old Problem
• Topological BF Theories in 3 and 4 Dimensions
• Plebanski Formulation of General Relativity: A Practical Introduction
• On the Relations between Gravity and BF Theories
• Form Geometry and the 'tHooft-Plebanski Action
• Gravity and Mirror Gravity in Plebanski Formulation
• Consistent matter couplings for Plebanski gravity
• Constraints and Reality Conditions in the Ashtekar Formulation of General Relativity
• Pure Connection Formulation, Twistors and the Chase for a Twistor Action for General Relativity
• Plebanski-like action for general relativity and anti-self-dual gravity