Anticommutativity Equation in Topological Quantum Mechanics

TL;DR

This paper explores topological quantum mechanics, demonstrating that its correlation functions satisfy an anticommutativity equation, which generalizes the commutativity condition and reveals new algebraic structures in topological field theories.

Contribution

It proves that the generating function of correlators in topological quantum mechanics satisfies an anticommutativity equation, extending known algebraic relations in topological field theories.

Findings

The generating function satisfies the anticommutativity equation $( abla - ext{F})^2=0$.

The commutativity equation $[dB, dB]=0$ is a special case of the anticommutativity equation.

The properties of topological quantum mechanics lead to new relations for topological correlators.

Abstract

We consider topological quantum mechanics as an example of topological field theory and show that its special properties lead to numerous interesting relations for topological corellators in this theory. We prove that the generating function $\mathcal{F}$ for thus corellators satisfies the anticommutativity equation $(\mathcal{D}- \mathcal{F})^2=0$. We show that the commutativity equation $[dB,dB]=0$ could be considered as a special case of the anticommutativity equation.