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On a Continuum Limit for Loop Quantum Cosmology · Around

2007

On a Continuum Limit for Loop Quantum Cosmology

Corichi, Alejandro, Vukasinac, Tatjana, Zapata, Jose A.

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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 the study of Loop Quantum Cosmology (LQC), a symmetry reduced theory that is related to Loop Quantum Gravity, and that is based on a non-regular, polymeric representation.
Recently, a soluble model was used by Ashtekar, Corichi and Singh to study the relation between Loop Quantum Cosmology and the standard Wheeler-DeWitt theory and in particular the passage to the limit in which the auxiliary parameter (interpreted as "quantum geometry discreetness") is sent to zero in hope to get rid of this `regulator ambiguity' in the LQC dynamics.
In this note we outline the first steps toward reformulating this question within the program developed by the authors for studying the continuum limit of polymeric theories, which was successfully applied to simple systems such as a Simple Harmonic Oscillator and the Free Particle.

Built on

Ashtekar A, Fairhurst S and Willis J L 2003 Quantum gravity, shadow states, and quantum mechanics Class. Quant. Grav. 20
2003
Earlier work this paper cites.
Ashtekar A 2007 An Introduction to Loop Quantum Gravity Through Cosmology Nuovo Cimento 112B
2005
Earlier work this paper cites.
Fleischhack C 2004 Representation of the Weyl algebra in quantum geometry [arXiv:math-ph/0407006]; Lewandowski J, Okolow A, Sahlmann H and Thiemann T 2006 Uniqueness of diffeomorphism invariant states on holonomy-flux algebras Comm. Math. Phys. 267
2006
Earlier work this paper cites.

Similar

Manrique E, Oeckl R, Weber A and Zapata J A 2006 Loop quantization as a continuum limit Class. Quant. Grav. 23
2006
Cited alongside, same era.
Ashtekar A, Lewandowski J 2004 Background independent quantum gravity: A status report Class. Quant. Grav. 21
2007
Cited alongside, same era.
Corichi A, Vukasinac T and Zapata J A 2007 Hamiltonian and Physical Hilbert space in polymer quantum mechanics Class. Quant. Grav. 24
2007
Cited alongside, same era.

Then

Ashtekar A, Corichi A and Singh P 2007 On the robustness of key features of loop quantum cosmology, [arXiv:0710.3565 [gr-qc]]
Original
2007
Closest in time.
Corichi A, Vukasinac T and Zapata J A 2007 Polymer quantum mechanics and its continuum limit Phys. Rev. D 76
Original
2007
Closest in time.

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