Is the Space-Time Non-Commutativity Simply Non-Commutativity of Derivatives?

Details Is the Space-Time Non-Commutativity Simply Non-Commutativity of Derivatives? Is the Space-Time Non-Commutativity Simply Non-Commutativity of Derivatives?

2003-08-16

arxiv.org/abs/math-ph/0308017v1

Proceedings of the 8th International Conference on Squeezed States and Uncertainty Relations. Puebla, Mexico. Eds. H. Moya-Ces

Physics

Mathematical Physics

8pp., no figures. Talk presented at the 8th International Conference on Squeezed States and Uncertainty Relations (ICSSUR'2003

Scientific paper

Recently, some problems have been found in the definition of the partial derivative in the case of the presence of both explicit and implicit functional dependencies in the classical analysis. In this talk we investigate the influence of this observation on the quantum mechanics and classical/quantum field theory. Surprisingly, some commutators of the coordinate-dependent operators are not equal to zero. Therefore, we try to provide mathematical foundations to the modern non-commutative theories. We also indicate possible applications in the Dirac-like theories.

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