Group contractions and its consequences upon representations of different spatial symmetry groups

2002/06/05 by Mauricio Ayala, Ayala, Mauricio, R. W. Haase +2
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #hep-th #math-ph #math.GR #math.MP #quant-ph

paper · pdf · doi:10.48550/arxiv.hep-th/0206037

To be published in the Proceedings of the Summer School "Geometric and Topological methods for Quantum Field Theory", Villa de Leyva, Colombia (2001)

arxiv created 2002/06/06 · arxiv updated 2009/11/30

Abstract

We investigate the group contraction method for various space-time groups, including SO(3)->E₂, SO(3,1)->G₃, SO(5-h,h)->P(3,1) (h=1 or 2), and its consequences for representations of these groups. Following strictly quantum mechanical procedures we specifically pay attention in the asymptotic limiting procedure employed in the contraction G -> G', not only to the respective algebras but to their representations spaces spanned by the eigenvectors of the Cartan subalgebra and the eigenvalues labelling these representation spaces. Where appropriate a physical interpretation is given to the contraction prodecure.

Citations

• Lie Groups, Lie Algebras, and Some of Their Applications

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