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Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext. 32700
Fax: 519-746-4319
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MC 6496
Giuseppe Sellaroli, Department of Applied Mathematics, University of Waterloo
Tensor operators for non-compact groups in loop quantum gravity
Tensor operators, in particular spinor ones, for SU(2) can been used in Euclidean loop quantum gravity as the building blocks for observables, in what is known as "spinor approach". In the (2+1) Lorentzian case, SU(2) must be replaced by the non-compact group SL(2,R), the double cover of the Lorentz group. I present the generalization of the usual results for tensor operators in this non-compact case; in particular I give an analogue of the well-known Wigner-Eckart theorem and the Jordan-Schwinger representation, and use them to construct the spinor formalism for LQG.
Contact Info
Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext. 32700
Fax: 519-746-4319
PDF files require Adobe Acrobat Reader
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