Do the Modified Uncertainty Principle and Polymer Quantization predict same physics?
Abstract
In this Letter we study the effects of the Modified Uncertainty Principle as proposed in Ali et al. (2009) [5] in simple quantum mechanical systems and study its thermodynamic properties. We have assumed that the quantum particles follow Maxwell-Boltzmann statistics with no spin. We compare our results with the results found in the GUP and polymer quantum mechanical frameworks. Interestingly we find that the corrected thermodynamic entities are exactly the same compared to the polymer results but the length scale considered has a theoretically different origin. Hence we express the need of further study for an investigation whether these two approaches are conceptually connected in the fundamental level.
- Publication:
-
Physics Letters B
- Pub Date:
- October 2012
- DOI:
- 10.1016/j.physletb.2012.09.035
- arXiv:
- arXiv:1207.6459
- Bibcode:
- 2012PhLB..717..291M
- Keywords:
-
- Generalized uncertainty principle;
- Minimal length;
- Statistical thermodynamics;
- Polymer quantum systems;
- General Relativity and Quantum Cosmology;
- Quantum Physics
- E-Print:
- 8 pages, comments and references added, accepted in Phys. Lett. B. arXiv admin note: text overlap with arXiv:1105.5314