Quantum Deformations of Einstein’s Relativistic Symmetries

  title={Quantum Deformations of Einstein’s Relativistic Symmetries},
  author={Jerzy Lukierski},
We shall outline two ways of introducing the modification of Einstein’s relativistic symmetries of special relativity theory — the Poincare symmetries. The most complete way of introducing the modifications is via the noncocommutative Hopf‐algebraic structure describing quantum symmetries. Two types of quantum relativistic symmetries are described, one with constant commutator of quantum Minkowski space coordinates (θμν‐deformation) and second with Lie‐algebraic structure of quantum space‐time… 

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Má slanka, Czech

  • J. Phys. 50,
  • 2000

nski, P

  • Máslanka, inFrom Field Theory to Quantum Groups , Eds. B. Jancewicz and J. Sobczyk, World Scientific,
  • 1996