# Quantum Identities for the Action

## TL;DR

This paper derives new identities involving the action functional in quantum mechanics, generalizing Ehrenfest's theorem and linking powers of the action with its derivatives in the path-integral framework.

## Contribution

It introduces novel identities relating the action functional and its derivatives, extending the theoretical understanding of quantum path integrals.

## Key findings

- New identities involving the action functional
- Generalizations of Ehrenfest's theorem
- Deeper insights into quantum path integrals

## Abstract

In this paper we derive various identities involving the {\it action} functional which enters the path-integral formulation of quantum mechanics. They provide some kind of generalisations of the Ehrenfest theorem giving correlations between powers of the action and its functional derivatives.