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Tensor operators for the Lorentz group in (2+1) loop quantum gravity

Jun 19
Group Seminar
4:00 pm o'clock to 5:00 pm o'clock
Giuseppe Sellaroli (University of Waterloo)
SR 02.729

Tensor operators for SU(2) can been used in 3D Euclidean loop quantum gravity as the building blocks for observables. 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. These results are then used to investigate if a Jordan-Schwinger representation always exists for SL(2,R), in order to carry on the techniques used in the Euclidean case.