---
abstract: 'The Wigner–Eckart theorem is a well known result for tensor operators of ${\mathrm{SU}}(2)$ and, more generally, any compact Lie group. This paper generalises it to arbitrary Lie groups, possibly non-compact. The result relies on 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.'
author:
- Giuseppe Sellaroli
bibliography:
- 'bibliography.bib'
title: '<span>Wigner–Eckart</span> theorem and <span>Jordan–Schwinger</span> representation for infinite-dimensional representations of the Lorentz group'
---

=1

Introduction
============

Representation theory {#sec:representation_theory}
=====================

Tensor Operators {#sec:tensor_operators}
================

Concluding remarks
==================

The author would like to thank Florian Girelli for introducing him to the topic and providing useful insights.

Notation
========

<span>Clebsch–Gordan</span> coefficients {#app:CG}
========================================

Tridiagonal matrices {#app:tridiagonal}
====================

{'source': 'arXiv_out/1509'}