Polymer Quantum Mechanics and its Continuum Limit

@article{Corichi2007PolymerQM,
  title={Polymer Quantum Mechanics and its Continuum Limit},
  author={Alejandro Corichi and Tatjana Vuka{\vs}inac and Jos{\'e} A. Zapata},
  journal={Physical Review D},
  year={2007},
  volume={76},
  pages={044016}
}
A rather nonstandard quantum representation of the canonical commutation relations of quantum mechanics systems, known as the polymer representation, has gained some attention in recent years, due to its possible relation with Planck scale physics. In particular, this approach has been followed in a symmetric sector of loop quantum gravity known as loop quantum cosmology. Here we explore different aspects of the relation between the ordinary Schroedinger theory and the polymer description. The… 

Semiclassical and quantum polymer effects in a flat isotropic universe

We analyze some relevant semiclassical and quantum features of the implementation of Polymer Quantum Mechanics to the phenomenology of the flat isotropic Universe. We firstly investigate a

Statistical Thermodynamics of Polymer Quantum Systems

Polymer quantum systems are mechanical models quantized similarly as loop quantum gravity. It is actually in quantizing gravity that the polymer term holds proper as the quantum geometry excitations

Polymer quantum mechanics as a deformation quantization

We analyze the polymer representation of quantum mechanics within the deformation quantization formalism. In particular, we construct the Wigner function and the star-product for the polymer

An open scattering model in polymerized quantum mechanics

We derive a quantum master equation in the context of a polymerized open quantum mechanical system for the scattering of a Brownian particle in an ideal gas environment. The model is formulated in a

Polymer Dirac field propagator: A model

Polymer quantum mechanics, the mechanical analogue of the loop quantization of gravity, has been applied recently to scalar field modes yielding interesting behavior for its corresponding propagator

Modular polymer representations of the Weyl algebra

One of the key conceptual challenges in quantum gravity is to understand how quantum theory should modify the very notion of spacetime. One way to investigate this question is to study the

On a Continuum Limit for Loop Quantum Cosmology

The use of non‐regular representations of the Heisenberg‐Weyl commutation relations has proved to be useful for studying conceptual and technical issues in quantum gravity. Of particular relevance is

On the choice of time in the continuum limit of polymeric effective theories

In polymeric quantum theories, a natural question pertains to the so called continuum limit, corresponding to the limit where the 'discreteness parameter' λ approaches zero. In particular one might

Ja n 20 19 Polymer Quantum Mechanics as a Deformation Quantization

We analyze the polymer representation of quantum mechanics within the deformation quantization formalism. In particular, we construct the Wigner function and the star-product for the polymer
...

References

SHOWING 1-10 OF 22 REFERENCES

Hamiltonian and physical Hilbert space in polymer quantum mechanics

In this paper, a version of polymer quantum mechanics, which is inspired by loop quantum gravity, is considered and shown to be equivalent, in a precise sense, to the standard, experimentally tested

Loop Quantum Cosmology

L loop quantum cosmology is an application of loop quantum gravity to homogeneous systems, which removes classical singularities and introduces the main effects of quantum effects into effective classical equations, which allow one to avoid the interpretational problems of quantum theory.

Quantum gravity, shadow states and quantum mechanics

A programme was recently initiated to bridge the gap between the Planck scale physics described by loop quantum gravity and the familiar low energy world. We illustrate the conceptual problems and

Quantum Nature of the Big Bang: Improved dynamics

An improved Hamiltonian constraint operator is introduced in loop quantum cosmology. Quantum dynamics of the spatially flat, isotropic model with a massless scalar field is then studied in detail

Singularity resolution in quantum gravity

We examine the singularity resolution issue in quantum gravity by studying a new quantization of standard Friedmann-Robertson-Walker geometrodynamics. The quantization procedure is inspired by the

Semiclassical states for quantum cosmology

In a metric variable based Hamiltonian quantization, we give a prescription for constructing semiclassical matter-geometry states for homogeneous and isotropic cosmological models. These 'collective'

Mathematical structure of loop quantum cosmology

Applications of Riemannian quantum geometry to cosmology have had notable successes. In particular, the fundamental discreteness underlying quantum geometry has led to a natural resolution of the big

Infrared singular fields and nonregular representations of canonical commutation relation algebras

Infrared singular variables which often enter in the formulation of models in quantum field theory, many‐body theory, and quantum statistical mechanics are described in terms of nonregular

Loop quantization as a continuum limit

We present an implementation of Wilson's renormalization group and a continuum limit tailored for loop quantization. The dynamics of loop-quantized theories is constructed as a continuum limit of the