Polymer Quantum Mechanics and its Continuum Limit
By Alejandro Corichi, T. Vukašinac, José A. Zapata. 2007
173 citations recorded by the source corpus.
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 paper has two parts. In the first one, we derive the polymer quantum mechanics starting from the ordinary Schroedinger theory and show that the polymer description arises as an appropriate limit. In the second part we consider the continuum limit of this theory, namely, the reverse process in which one starts from the discrete theory and tries to recover back the ordinary Schroedinger quantum mechanics. We consider several examples of interest, including the harmonic oscillator, the free particle, and a simple cosmological model.
Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/596e5276e4d36c6f4891d0c286f55ce79e682c50
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In Atomic and Molecular Physics, and Optics
- Parampreet Singh
- Abhay Ashtekar
- Alejandro Corichi
- E. Wilson-Ewing
- Carlo Rovelli
- Sergei D. Odintsov
- Kazuharu Bamba
- Gianluca Calcagni
In Nuclear and High Energy Physics
- Abhay Ashtekar
- Parampreet Singh
- Alejandro Corichi
- M. Bojowald
- E. Wilson-Ewing
- Sergei D. Odintsov
- Kazuharu Bamba
- Iván Agulló
In Statistical and Nonlinear Physics
- Abhay Ashtekar
- Parampreet Singh
- Alejandro Corichi
- E. Wilson-Ewing
- M. Bojowald
- Sergei D. Odintsov
- Kazuharu Bamba
- Carlo Rovelli
Citations in the corpus
- Robustness of key features of loop quantum cosmology (2007, result): “24, 1495 (2007), arXiv:gr-qc/0610072 [18] A.”
- Loop quantum cosmology: a status report (2011, result): “This is in striking contrast to the examples in ‘polymer quantum mechanics’ [137, 138, 147] and lattice gauge theories where a continuum limit does exists when discreteness parameter is sent to zero.”