Angular momentum non conserving symmetries in bosonic models

TL;DR

This paper classifies new angular momentum non-conserving symmetries in bosonic quantum models using Lie algebra decompositions and Dynkin diagrams, revealing unexpected spinor structures.

Contribution

It introduces a complete classification of AMNC dynamical symmetries in bosonic models via Lie algebra and Dynkin diagram analysis, and explores their implications.

Findings

Identification of conjugacy classes of A_1 subalgebras

Discovery of unexpected spinor structures in bosonic models

Development of new bases for diagonalization

Abstract

The Levi-Malcev decomposition is applied to bosonic models of quantum mechanics based on unitary Lie algebras u(2), u(2)+u(2), u(3) and u(4) to clearly disentangle semisimple subalgebras. The theory of weighted Dynkin diagrams is then applied to identify conjugacy classes of relevant A_1 subalgebras allowing to introduce a complete classification of new angular momentum non conserving (AMNC) dynamical symmetries. The tensor analysis of the whole algebra based on the new "angular momentum" operators reveals unexpected spinors to occur in purely bosonic models. The new chains of subalgebra can be invoked to set up ANMC bases for diagonalization.