Area expectation values in quantum area Regge calculus

Abstract

The Regge calculus generalised to independent area tensor variables is considered. The continuous time limit is found and formal Feynman path integral measure corresponding to the canonical quantisation is written out. The quantum measure in the completely discrete theory is found which possesses the property to lead to the Feynman path integral in the continuous time limit whatever coordinate is chosen as time. This measure can be well defined by passing to the integration over imaginary field variables (area tensors). Averaging with the help of this measure gives finite expectation values for areas.

9 pages, LaTeX, possible relation to quantisation of the usual length-based Regge calculus is discussed

References in corpus (7)

• Discrete approaches to quantum gravity in four dimensions
• Discrete structures in gravity
• The basis of the Ponzano-Regge-Turaev-Viro-Ooguri model is the loop representation basis
• A note on area variables in Regge calculus
• Regge calculus in the canonical form
• How to construct quantum measure in Regge calculus?
• Area Regge calculus and continuum limit

Cited by in corpus (12)

• Regge calculus from discontinuous metrics
• One more variant of discrete gravity having "naive" continual limit
• On the length expectation values in quantum Regge calculus
• Exact Bianchi Identity in Regge Gravity
• On the non-perturbative graviton propagator
• Integration over connections in the discretized gravitational functional integrals
• On the possibility of finite quantum Regge calculus
• Path integral in area tensor Regge calculus and complex connections
• Discrete quantum gravity in the framework of Regge calculus formalism
• On the area expectation values in area tensor Regge calculus in the Lorentzian domain
• Feynman path integral in area tensor Regge calculus and correspondence principle
• On positivity of quantum measure and of effective action in area tensor Regge calculus