A.E.Shalyt-Margolin. Minimal Length, Measurable and Nonmeasurable Quantities, and Mathematical Apparatus of Quantum Theory I
Natural Sciences / Physics / Quantum field theory
Submitted on: Feb 04, 2015, 05:16:40
Description: In this paper it is supposed that the theory involves a minimal length. Within the scope of this supposition, for the case of a free particle, the notions of measurability and measurable quantities are used as a basis for a mathematical apparatus of a new theory that is a deformation of the conventional (nonrelativistic) quantum mechanics. Consideration is given to one example from gravity with two different but very close low-energy limits: (1) continuous limit based on the use of nonmeasurable quantities;(2) discrete limit based on the use of measurable quantities. In conclusion the main course for further studies is defined. The paper is a continuation of the earlier studies conducted by the author and of his latest publication devoted to the inferences concerning the introduction of a minimal length in a quantum theory and in gravity.