Symmetric polynomials in physics

TL;DR

This paper explores the role of symmetric polynomials in physics, specifically in quantum gases and phase space quantization, revealing their importance in thermodynamics and mathematical physics.

Contribution

It provides two novel examples demonstrating the significance of symmetric polynomials in physical theories and their interpretations.

Findings

Partition functions of ideal quantum gases relate to symmetric polynomials

Symmetric polynomials appear in Berezin's phase space quantization

Thermodynamical interpretation of symmetric polynomial theory

Abstract

We give two examples where symmetric polynomials play an important role in physics: First, the partition functions of ideal quantum gases are closely related to certain symmetric polynomials, and a part of the corresponding theory has a thermodynamical interpretation. Further, the same symmetric polynomials also occur in Berezin's theory of quantization of phase spaces with constant curvature.