Spinor operators in 2+1 Lorentzian loop quantum gravity
by
Giuseppe Sellaroli(Università di Waterloo)
→
Europe/Rome
2N44 (Dipartimento di Fisica)
2N44
Dipartimento di Fisica
Description
Tensor operators, in particular spinor ones, for SU(2) can be 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.