Phase Space on a Noncommutative de Sitter Spacetime

De Matos Espírito Santo, João Paulo (2024) Phase Space on a Noncommutative de Sitter Spacetime. Bachelor's Thesis, Physics.

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Abstract

In this thesis, an exploration of formulations of phase space in a non-commutative de Sitter spacetime is undergone. Mappings between classical phase space and quantum mechanics are discussed. Methods of defining a phase space in a Lorentz-violating noncommutative de Sitter space are considered and its spacetime symmetries are discussed. An overview of classical phase space and its QM formulation is given through Weyl quantization and the Groenewold-Moyal bracket. Different bracket structures are explored for the case of the Poisson and Groenewold-Moyal bracket. It’s demonstrated that the Jacobi identity of both the Groenewold-Moyal bracket and the Dirac commutator in a noncommutative Minkowski spacetime requires a constant self-commutator of the 4-position operators. A short introduction to de Sitter spacetime, its group and algebra is given. It’s concluded that a noncommutative de Sitter spacetime lacks both complete Lorentz symmetry and translational invariance. It is speculated that, in contrast to the case of a noncommutative Minkowski space- time, the de Sitter momentum operator and its commutation relations lead to the Jacobi Identity demanding a non-constant self-commutator of 4-position operators. It is finally concluded that to define a phase space on a noncommutative de Sitter spacetime, its symmetry group and algebra must first be explicitly defined.

Item Type:	Thesis (Bachelor's Thesis)
Supervisor name:	Boer, D.
Degree programme:	Physics
Thesis type:	Bachelor's Thesis
Language:	English
Date Deposited:	16 Jul 2024 11:18
Last Modified:	16 Jul 2024 11:18
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/33443

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