# Polymer quantization and the saddle point approximation of partition functions

@article{MoralesTecotl2015PolymerQA, title={Polymer quantization and the saddle point approximation of partition functions}, author={Hugo A. Morales-T'ecotl and Daniel H. Orozco-Borunda and Saeed Rastgoo}, journal={Physical Review D}, year={2015}, volume={92}, pages={104029} }

The saddle point approximation of the path integral partition functions is an important way of deriving the thermodynamical properties of black holes. However, there are certain black hole models and some mathematically analog mechanical models for which this method cannot be applied directly. This is due to the fact that their action evaluated on a classical solution is not finite and its first variation does not vanish for all consistent boundary conditions. These problems can be dealt with…

## 14 Citations

### Polymerization, the Problem of Access to the Saddle Point Approximation, and Thermodynamics

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This work seeks an alternative solution to the saddle point approximation to the partition functions via the polymer quantization which is motivated by the loop quantum gravity.

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### Perturbative polymer quantum field theory and high energy scalar propagator

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We advance a proposal of perturbative polymer field theory motivated by the study of the high energy regime of scalar propagator in flat spacetime. To do so we revisit the model by Hossain, Husain…

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The classical Raychaudhuri equation predicts the formation of conjugate points for a congruence of geodesics, in a finite proper time. This in conjunction with the Hawking-Penrose singularity…

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- Physics
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We have computed, using instanton methods, the first allowed energy band for the polymer harmonic oscillator. The eigenvalues within the band are labelled by a discrete parameter λ which results from…

### Deformed algebra and the effective dynamics of the interior of black holes

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We consider the classical Hamiltonian of the interior of the Schwarzschild black hole in Ashtekar–Barbero connection formalism. Then, inspired by generalized uncertainty principle models, we deform…

### A model of polymer gravitational waves: Theory and some possible observational consequences

- PhysicsThe Sixteenth Marcel Grossmann Meeting
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We propose a polymer quantization scheme to derive the eﬀective propagation of gravitational waves on a classical Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime. These waves, which may…

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The linearized Einstein field equations provide a low energy wave equation for propagation of gravitational fields which may be originated from a high energy source. Motivated by loop quantum gravity…

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- PhysicsThe Sixteenth Marcel Grossmann Meeting
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We show that loop quantum gravity eﬀects leads to the ﬁniteness of expansion and its rate of change in the eﬀective regime in the interior of the Schwarzschild black hole. As a consequence the…

### Black hole singularity resolution via the modified Raychaudhuri equation in loop quantum gravity

- Physics
- 2020

We derive Loop Quantum Gravity corrections to the Raychaudhuri equation in the interior of a Schwarzschild black hole and near the classical singularity. We show that the resulting effective equation…

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