Families of vector-like deformations of relativistic quantum phase spaces, twists and symmetries
| Autor: | Daniel Meljanac, Stjepan Meljanac, Danijel Pikutić |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | European Physical Journal C: Particles and Fields, Vol 77, Iss 12, Pp 1-12 (2017) |
| Druh dokumentu: | article |
| ISSN: | 1434-6044 1434-6052 |
| DOI: | 10.1140/epjc/s10052-017-5373-9 |
| Popis: | Abstract 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 $$\mathfrak {gl}(n)$$ 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) $$\kappa $$ κ -Minkowski spaces and (iii) $$\kappa $$ κ -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. |
| Databáze: | Directory of Open Access Journals |
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