Classical and Quantal Ternary Algebras

TL;DR

This paper compares classical and quantum ternary algebras relevant to physics, illustrating how classical limits can be obtained from quantal algebras via contraction, exemplified by the Virasoro-Witt algebra.

Contribution

It introduces a method to derive classical ternary algebras from their quantum counterparts through contraction, with explicit examples.

Findings

Classical and quantum ternary algebras are compared and contrasted.

Classical limits of certain infinite algebras can be obtained via contraction of the quantum algebra.

The Virasoro-Witt algebra is used as an example to illustrate the contraction process.

Abstract

We consider several ternary algebras relevant to physics. We compare and contrast the quantal versions of the algebras, as realized through associative products of operators, with their classical counterparts, as realized through classical Nambu brackets. In some cases involving infinite algebras, we show the classical limit may be obtained by a contraction of the quantal algebra, and then explicitly realized through classical brackets. We illustrate this classical-contraction method by the Virasoro-Witt example.