IDENTICAL PARTICLES AND PERMUTATION GROUP

TL;DR

This paper revisits second quantization, showing creation and annihilation operators relate to both the algebra h(1) and the superalgebra osp(1|2), revealing differences in many-particle cases and suggesting potential for unorthodox quantum field theories.

Contribution

It demonstrates the equivalence of h(1) and osp(1|2) in one-mode sectors and explores their implications for Bose and Fermi statistics, proposing new avenues for quantum field theory.

Findings

Algebra h(1) and osp(1|2) are equivalent in one-mode sectors.

Differences arise in many-particle cases due to grading of osp(1|2).

Potential for unorthodox quantum field theories is identified.

Abstract

Second quantization is revisited and creation and annihilation operators are shown to be related, on the same footing both to the algebra ${\it h}(1)$, ${\underline {and}}$ to the superalgebra ${\it osp}(1|2)$ that are shown to be both compatible with Bose ${\underline {and}}$ Fermi statistics. The two algebras are completely equivalent in the one-mode sector but, because of grading of ${\it osp}(1|2)$, differ in the many-particle case. The possibility of a unorthodox quantum field theory is suggested.