MC 6496
Speaker
GiuseppeÌýSellaroli, Department of Applied Mathematics, University of À¶Ý®ÊÓƵ
Title
Tensor operators for non-compact groups in loop quantum gravity
Abstract
Tensor operators, in particular spinor ones, for SU(2) can been usedÌýin Euclidean loop quantum gravity as the building blocks forÌýobservables, in what is known as "spinor approach". In the (2+1)ÌýLorentzian case, SU(2) must be replaced by the non-compact groupÌýSL(2,R), the double cover of the Lorentz group. I present theÌýgeneralization of the usual results for tensor operators in thisÌýnon-compact case; in particular I give an analogue of the well-knownÌýWigner-Eckart theorem and the Jordan-Schwinger representation, and useÌýthem to construct the spinor formalism for LQG.