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Advances in High Energy Physics
Volume 2014, Article ID 195157, 8 pages
http://dx.doi.org/10.1155/2014/195157
Research Article

Minimal Length and the Existence of Some Infinitesimal Quantities in Quantum Theory and Gravity

National Centre of Particles and High Energy Physics, Pervomayskaya Street 18, 220088 Minsk, Belarus

Received 23 September 2014; Accepted 25 November 2014; Published 10 December 2014

Academic Editor: George Siopsis

Copyright © 2014 A. E. Shalyt-Margolin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.

Abstract

It is demonstrated that provided a theory involves a minimal length, this theory must be free from such infinitesimal quantities as infinitely small variations in surface of the holographic screen, its volume, and entropy. The corresponding infinitesimal quantities in this case must be replaced by the “minimal variations possible”—finite quantities dependent on the existent energies. As a result, the initial low-energy theory (quantum theory or general relativity) inevitably must be replaced by a minimal length theory that gives very close results but operates with absolutely other mathematical apparatus.