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

Khatsymovsky, V. M.

doi:10.1016/j.physletb.2005.12.033

Physics Letters B

2006

DOI: 10.1016/j.physletb.2005.12.033

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

V. M. Khatsymovsky

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.

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Cited by 2 publications

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The phase and critical point of quantum Einstein–Cartan gravity

Xue

2012

Physics Letters B

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By introducing diffeomorphism and local Lorentz gauge invariant holonomy fields, we study in the recent article [S.-S. Xue, Phys. Rev. D82 (2010) 064039] the quantum EinsteinCartan gravity in the framework of Regge calculus. On the basis of strong coupling expansion, mean-field approximation and dynamical equations satisfied by holonomy fields, we present in this Letter calculations and discussions to show the phase structure of the quantum Einstein-Cartan gravity, (i) the order phase: long-range condensations of holonomy fields in strong gauge couplings; (ii) the disorder phase: short-range fluctuations of holonomy fields in weak gauge couplings. According to the competition of the activation energy of holonomy fields and their entropy, we give a simple estimate of the possible ultra-violet critical point and correlation length for the second-order phase transition from the order phase to disorder one. At this critical point, we discuss whether the continuum field theory of quantum Einstein-Cartan gravity can be possibly approached when the macroscopic correlation length of holonomy field condensations is much larger than the Planck length.

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The phase and critical point of quantum Einstein–Cartan gravity

Xue

2012

Physics Letters B

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Detailed discussions and calculations of quantum Regge calculus of Einstein-Cartan theory

Xue

2010

Phys. Rev. D

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This article presents detailed discussions and calculations of the recent paper ''Quantum Regge calculus of Einstein-Cartan theory'' in [9]. The Euclidean space-time is discretized by a four-dimensional simplicial complex. We adopt basic tetrad and spin-connection fields to describe the simplicial complex. By introducing diffeomorphism and local Lorentz invariant holonomy fields, we construct a regularized Einstein-Cartan theory for studying the quantum dynamics of the simplicial complex and fermion fields. This regularized Einstein-Cartan action is shown to properly approach to its continuum counterpart in the continuum limit. Based on the local Lorentz invariance, we derive the dynamical equations satisfied by invariant holonomy fields. In the mean-field approximation, we show that the averaged size of 4-simplex, the element of the simplicial complex, is larger than the Planck length. This formulation provides a theoretical framework for analytical calculations and numerical simulations to study the quantum Einstein-Cartan theory.

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

Cited by 2 publications

References 19 publications

The phase and critical point of quantum Einstein–Cartan gravity

The phase and critical point of quantum Einstein–Cartan gravity

Detailed discussions and calculations of quantum Regge calculus of Einstein-Cartan theory

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