On the area expectation values in area tensor Regge calculus in the Lorentzian domain

TL;DR

This paper investigates the Wick rotation in area tensor Regge calculus, confirming that Lorentzian and Euclidean measures on spacelike areas coincide, supporting the probabilistic interpretation of the Lorentzian measure.

Contribution

It demonstrates the equivalence of Lorentzian and Euclidean measures in area tensor Regge calculus for spacelike areas, validating the probabilistic interpretation.

Findings

Lorentzian measure coincides with Euclidean measure on spacelike areas

Wick rotation confirms measure equivalence in Lorentzian domain

Supports probabilistic interpretation of Lorentzian measure

Abstract

Wick rotation in area tensor Regge calculus is considered. The heuristical expectation is confirmed that the Lorentzian quantum measure on a spacelike area should coincide with the Euclidean measure at the same argument. The consequence is validity of probabilistic interpretation of the Lorentzian measure as well (on the real, i.e. spacelike areas).