Noncommutative pfaffians and classification of states of five-dimensional quasi-spin

TL;DR

This paper introduces a new quantum number for classifying states of a five-dimensional quasi-spin system using noncommutative pfaffians from orthogonal algebra, expanding the tools for quantum state classification.

Contribution

It constructs a novel quantum number based on noncommutative pfaffians, providing a new method for classifying five-dimensional quasi-spin states.

Findings

Defined a new quantum number using pfaffians

Classified states of five-dimensional quasi-spin

Linked pfaffians to creation operators in quantum algebra

Abstract

Noncommutative pfaffians associated with an orthogonal algebra $\mathfrak{o}_N$ are some special elements of the universal enveloping algebra $U(\mathfrak{o}_N)$. Using pfaffians we construct the fourth quantum number which together with the naturally defined three quantum numbers allow to classify the states of a five-dimensional quasi-spin. The pfaffians are treated as creation operators for the new quantum number.