Abstract
I shall recall in historical perspective some results from nineties and show further how κ-deformed symmetries and κ-Minkowski space inspired DSR (Doubly of Deformed Special Relativity) approach proposed after 2000. As very recent development I shall show how to describe quantum-covariant κ-deformed phase spaces by passing from Hopf algebras to Hopf algebroids (arXiv:1507.02612) and I will briefly describe the κ-deformations of AdS5 × S5 superstring target spaces (arXiv:1510.030.83).
Highlights
Transition from classical to quantum physics leads to the appearance of noncommutative algebraic structures
In standard quantum mechanics (QM) the canonical quantum phase space is described by Heisenberg algebra (HA) (i,j=1,2,3)
One can localize separately the positions or momenta with arbitrary accuracy, what is reflected in the use in QM of classical geometry, with commutative space and time
Summary
Transition from classical to quantum physics leads to the appearance of noncommutative algebraic structures. In previous Section we presented H as κ-Poincare-Hopf algebra describing deformed relativistic space-time symmetries; below we shall introduce quantum κ-Poincare group Has its dual Hopf-algebra.
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