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A proposal of quantization in flat space‐time with a minimal length present
Author(s) -
Hess P.O.
Publication year - 2015
Publication title -
astronomische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.394
H-Index - 63
eISSN - 1521-3994
pISSN - 0004-6337
DOI - 10.1002/asna.201512218
Subject(s) - quantization (signal processing) , algebraic number , space (punctuation) , dimension (graph theory) , algebraic structure , theoretical physics , physics , simple (philosophy) , extension (predicate logic) , classical mechanics , quantum , algebra over a field , mathematics , computer science , quantum mechanics , pure mathematics , mathematical analysis , algorithm , philosophy , epistemology , programming language , operating system
The 4‐dimensional space‐time is extended to pseudo‐complex coordinates. Proposing the standard quantization rules in this extended space, the ones for the 4‐dimensional sub‐space acquire, as one solution, the commutation relations with non‐commuting coordinates. This demonstrates that the algebraic extension keeps the simple structure of Quantum Mechanics, while it also introduces an effective quite involved structure in the 4‐dimensional sub‐space. The first steps to pseudo‐complex Quantum Mechanics in 1‐dimension are outlined, awaiting still the interpretation of some new emerging structures. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)