# Quantum integrability for the Beltrami-Laplace operators of projectively equivalent metrics of arbitrary signatures

## TL;DR

This paper extends the understanding of quantum integrability by showing that Killing tensors from projectively equivalent metrics lead to commuting differential operators across all signatures.

## Contribution

It generalizes previous results to all metric signatures, establishing a link between Killing tensors and commuting differential operators in quantum integrability.

## Key findings

- Killing tensors from projectively equivalent metrics correspond to commuting differential operators
- The generalization applies to metrics of arbitrary signatures
- Supports the broader applicability of quantum integrability principles

## Abstract

We generalize the result of [Matveev-Topalov 2001] to all signatures: we show that in all signatures the Killing tensors constructed by projectively equivalent metrics correspond to commuting differential operators