New concept of relativistic invariance in noncommutative space-time: twisted poincare symmetry and its implications.

@article{Chaichian2004NewCO,
  title={New concept of relativistic invariance in noncommutative space-time: twisted poincare symmetry and its implications.},
  author={Masud Chaichian and Peter Pre{\vs}najder and Anca Tureanu},
  journal={Physical review letters},
  year={2004},
  volume={94 15},
  pages={
          151602
        }
}
We present a systematic framework for noncommutative (NC) quantum field theory (QFT) within the new concept of relativistic invariance based on the notion of twisted Poincare symmetry, as proposed by Chaichian et al. [Phys. Lett. B 604, 98 (2004)]. This allows us to formulate and investigate all fundamental issues of relativistic QFT and offers a firm frame for the classification of particles according to the representation theory of the twisted Poincare symmetry and as a result for the NC… 

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References

SHOWING 1-10 OF 13 REFERENCES

On a Lorentz- Invariant Interpretation of Quantum Field Theory on Noncommutative Noncommutative Space-Time

  • On a Lorentz- Invariant Interpretation of Quantum Field Theory on Noncommutative Noncommutative Space-Time

Jost-Lehmann-Dyson Representation and Froissart-Martin Bound in Quantum Field Theory on Noncommutative Space-Time

In the framework of quantum field theory (QFT) on noncommutative (NC) space-time with $SO(1,1)\times SO(2)$ symmetry, which is the feature arising when one has only space-space noncommutativity

Demichev Quantum Groups A Guide to Quantum Groups

  • World Scientific
  • 1994

Phys. Lett. B

  • Phys. Lett. B
  • 2003

Deformed Coordinate Spaces Derivatives, hep-th/0408080

  • Deformed Coordinate Spaces Derivatives, hep-th/0408080

Commun. Math. Phys

  • Commun. Math. Phys
  • 1995

Mat. Fys. Medd

  • Mat. Fys. Medd
  • 1955

Int. J. Mod

  • Int. J. Mod
  • 2000