PIRSA:16100050

Video URL

https://pirsa.org/16100050

Wigner-Eckart theorem and Jordan-Schwinger representation for infinite-dimensional representations of the Lorentz group

Sellaroli, G. (2016). Wigner-Eckart theorem and Jordan-Schwinger representation for infinite-dimensional representations of the Lorentz group. Perimeter Institute for Theoretical Physics. https://pirsa.org/16100050

Sellaroli, Giuseppe. Wigner-Eckart theorem and Jordan-Schwinger representation for infinite-dimensional representations of the Lorentz group. Perimeter Institute for Theoretical Physics, Oct. 27, 2016, https://pirsa.org/16100050 

          @misc{ scivideos_PIRSA:16100050,
            doi = {10.48660/16100050},
            url = {https://pirsa.org/16100050},
            author = {Sellaroli, Giuseppe},
            keywords = {Mathematical physics},
            language = {en},
            title = {Wigner-Eckart theorem and Jordan-Schwinger representation for infinite-dimensional representations of the Lorentz group},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2016},
            month = {oct},
            note = {PIRSA:16100050 see, \url{https://scivideos.org/pirsa/16100050}}
          }

Giuseppe Sellaroli

Talk numberPIRSA:16100050
DOI10.48660/16100050
Source RepositoryPIRSA
Collection
Talk Type Scientific Series
Subject

Abstract

The Wigner-Eckart theorem is a well known result for tensor operators of SU(2) and, more generally, any compact Lie group. I will show how it can be generalised to arbitrary Lie groups, possibly non-compact. The result relies on the knowledge of recoupling theory between finite-dimensional and arbitrary admissible representations, which may be infinite-dimensional; the particular case of the Lorentz group will be studied in detail. As an application, the Wigner-Eckart theorem will be used to construct an analogue of the Jordan-Schwinger representation, previously known only for finite-dimensional representations of the Lorentz group, valid for infinite-dimensional ones.