Video URL
https://pirsa.org/16100050Wigner-Eckart theorem and Jordan-Schwinger representation for infinite-dimensional representations of the Lorentz group
APA
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
MLA
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
BibTex
@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/index.php/pirsa/16100050}} }
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.