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Families of vector-like deformations of relativistic quantum phase spaces, twists and symmetries

Meljanac, Daniel; Meljanac, Stjepan; Pikutić, Danijel (2017) Families of vector-like deformations of relativistic quantum phase spaces, twists and symmetries. European physical journal C : particles and fields, 77 (12). ISSN 1434-6044

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Families of vector-like deformed relativistic quantum phase spaces and corresponding realizations are analyzed. A method for a general construction of the star product is presented. The corresponding twist, expressed in terms of phase space coordinates, in the Hopf algebroid sense is presented. General linear realizations are considered and corresponding twists, in terms of momenta and Poincaré–Weyl generators or gl(n) generators are constructed and R-matrix is discussed. A classification of linear realizations leading to vector-like deformed phase spaces is given. There are three types of spaces: (i) commutative spaces, (ii) kappa-Minkowski spaces and (iii) kappa-Snyder spaces. The corresponding star products are (i) associative and commutative (but non-local), (ii) associative and non-commutative and (iii) non-associative and non-commutative, respectively. Twisted symmetry algebras are considered. Transposed twists and left–right dual algebras are presented. Finally, some physical applications are discussed.

Item Type: Article
Uncontrolled Keywords: noncommutative space
Subjects: NATURAL SCIENCES > Physics
Divisions: Division of Materials Physics
Theoretical Physics Division
Project titleProject leaderProject codeProject type
prema kvantnoj gravitaciji: nekomutativna geometrija, teorija polja i kozmologija-tqgngftcStjepan MeljanacIP-2014-09-9582HRZZ
Depositing User: Daniel Meljanac
Date Deposited: 18 Jan 2018 17:22
DOI: 10.1140/epjc/s10052-017-5373-9

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