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

Abstract

Families of vector-like deformed relativistic quantum phase spaces and corresponding realizations are analyzed. Method for general construction of star product is presented. Corresponding twist, expressed in terms of phase space coordinates, in Hopf algebroid sense is presented. General linear realizations are considered and corresponding twists, in terms of momenta and Poincaré-Weyl generators or $\mathfrak{gl}(n)$ generators, are constructed and R-matrix is discussed. Classification of linear realizations leading to vector-like deformed phase spaces is given. There are 3 types of spaces: $i)$ commutative spaces, $ii)$ $\kappa$-Minkowski spaces and $iii)$ $\kappa$-Snyder spaces. 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.

20 pages, version accepted for publication in EPJC

References in corpus (8)

• New realizations of Lie algebra kappa-deformed Euclidean space
• Twisted Statistics in kappa-Minkowski Spacetime
• Deformed Special Relativity and Deformed Symmetries in a Canonical Framework
• Deformed Oscillator Algebras and QFT in $\kappa$-Minkowski Spacetime
• kappa-Minkowski spacetime as the result of Jordanian twist deformation
• Twisting all the way: from Classical Mechanics to Quantum Fields
• Scalar field theory in Snyder space-time: alternatives
• Kappa Snyder deformations of Minkowski spacetime, realizations and Hopf algebra

Cited by in corpus (1)

• $\kappa$-deformed phase spaces, Jordanian twists, Lorentz-Weyl algebra and dispersion relations