On the possibility of finite quantum Regge calculus

Khatsymovsky, V. M.

doi:10.1016/j.physletb.2007.06.039

Cited by 5 publications

(3 citation statements)

References 15 publications

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“…This agrees with the fact that the measures on the metric in the continuum GR are generally defined up to a power of − det g λµ [25,26]. We can write [27] the general form of this factor which is a scalar density symmetrically as…”

Section: The Results Of the Functional Integration Over Connectionsupporting

confidence: 78%

“…, are also present in the simplicial measure F (ℓ)d n ℓ, since we have the same formula (27) in each 4-simplex, but the number of the leaf/diagonal triangle areas which are fixed by maximizing the measure is now sufficient to fixe the leaf/diagonal edge lengths. Therefore, these determinant-type factors are not shown in the estimate for F (ℓ)d n ℓ (25) as compared with the dependence on v, which has more pronounced maxima for large η.…”

Section: The Results Of the Functional Integration Over Connectionmentioning

confidence: 99%

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On the non-perturbative graviton propagator

Khatsymovsky

2018

Preprint

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To reduce general relativity to the canonical Hamiltonian formalism and construct the path (functional) integral in a simpler and, especially in the discrete case, less singular way, one extends the configuration superspace, as in the connection representation. Then we perform functional integration over connection.The module of the result of this integration arises in the leading order of the expansion over a scale of the discrete lapse-shift functions and has maxima at finite (Planck scale) areas/lengths and rapidly decreases at large areas/lengths, as we have mainly considered previously; the phase arises in the leading order (Regge action) of the stationary phase expansion. Now we consider the possibility of confining ourselves to these leading terms in a certain region of the parameters of the theory; consider background edge lengths as an optimal starting point for the perturbative expansion of the theory; estimate the background length scale and consider the form of the graviton propagator. In parallel with the general simplicial structure, we consider the simplest periodic simplicial structure with a part of the variables frozen ("hypercubic"), for which also the propagator in the leading approximation over metric variations can be written in a closed form.

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Section: The Results Of the Functional Integration Over Connectionsupporting

confidence: 78%

Section: The Results Of the Functional Integration Over Connectionmentioning

confidence: 99%

On the non-perturbative graviton propagator

Khatsymovsky

2018

Preprint

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“…Our strategy (briefly reviewed in [7]) is based on the requirement for the full discrete measure to result in the canonical Hamiltonian functional integral measure with time t, with some coordinate chosen as t and made continuous.…”

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confidence: 99%

Barbero-Immirzi parameter in Regge calculus

Khatsymovsky

2008

Preprint

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We consider Regge calculus in the representation in terms of area tensors and self-and antiselfdual connections generalised to the case of Holst action that is standard Einstein action in the tetrad-connection variables plus topological (on equations of motion for connections) term with coefficient 1/γ, γ is Barbero-Immirzi parameter. The quantum measure is shown to exponentially decrease with areas with typical cut-off scales 4πG and 4πGγ in spacelike and timelike regions, respectively (G is the Newton constant).

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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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On the possibility of finite quantum Regge calculus

Cited by 5 publications

References 15 publications

On the non-perturbative graviton propagator

On the non-perturbative graviton propagator

Barbero-Immirzi parameter in Regge calculus

The phase and critical point of quantum Einstein–Cartan gravity

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