Quantum Regge Calculus of Einstein-Cartan theory

Understand

We study the Quantum Regge Calculus of Einstein-Cartan theory to describe quantum dynamics of Euclidean space-time discretized as a 4-simplices complex.

• Tetrad field e_\mu(x) and spin-connection field \omega_\mu(x) are assigned to each 1-simplex.
• Applying the torsion-free Cartan structure equation to each 2-simplex, we discuss parallel transports and construct a diffeomorphism and {\it local} gauge-invariant Einstein-Cartan action.
• Invariant holonomies of tetrad and spin-connection fields along large loops are also given.