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Field theory on noncommutative spaces of general form

Abstract

A combination of quantum mechanics with general relativity indicates that on the distances of the order of Planck length the space-time is nonlocal and can be described by a sort of noncommutative structure. The aim of this project is to study the physical consequences of the noncommutativity of the general form, when the commutator of coordinates depends on these coordinates and (or) momenta. Using as the mathematical basis the model of relativistic quantum mechanics, recently proposed by the author of the project, we are planing to advance in the direction of the construction of consistent quantum field theory on noncommutative spaces of generic form. The subjects of the particular interest are: the realization of physical symmetries on this type of noncommutative spaces and the deduction of the corresponding conservation laws. The study of particular models of noncommutative spaces, such as, the noncommutative space defined as a foliation of three-dimensional euclidean space by a fuzzy spheres, the Snyder space-time, etc. The analyzes of the renormalization properties of the field theoretical models with the explicit form of the star product. The study of the physical mechanisms which determine the noncommutativity. (AU)

Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
KUPRIYANOV, V. G. Weak associativity and deformation quantization. Nuclear Physics B, v. 910, p. 240-258, SEP 2016. Web of Science Citations: 4.
KUPRIYANOV, V. G.; VASSILEVICH, D. V. Nonassociative Weyl star products. Journal of High Energy Physics, n. 9 SEP 16 2015. Web of Science Citations: 15.

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