Tensor and Spin Representations of SO(4) and Discrete Quantum Gravity

  • M. Lorente
  • P. Kramer
Conference paper

DOI: 10.1007/1-4020-2634-X_18

Cite this paper as:
Lorente M., Kramer P. (2004) Tensor and Spin Representations of SO(4) and Discrete Quantum Gravity. In: Gruber B.J., Marmo G., Yoshinaga N. (eds) Symmetries in Science XI. Springer, Dordrecht

Abstract

Starting from the defining transformations of complex matrices for the SO(4) group, we construct the fundamental representation and the tensor and spinor representations of the group SO(4). Given the commutation relations for the corresponding algebra, the unitary representations of the group in terms of the generalized Euler angles are constructed. These mathematical results help us to a more complete description of the Barret-Crane model in Quantum Gravity. In particular a complete realization of the weight function for the partition function is given and a new geometrical interpretation of the asymptotic limit for the Regge action is presented.

Keywords

SO(4) group tensor representation spin representation quantum gravity spin networks 

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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • M. Lorente
    • 1
  • P. Kramer
    • 2
  1. 1.Departamento de FísicaUniversidad de OviedoOviedoSpain
  2. 2.Institut für theoretische PhysikUniversität TübingenTübingenGermany

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