# Local Lorentz covariance in finite-dimensional Local Quantum Physics

## TL;DR

This paper demonstrates that local Lorentz covariance naturally emerges from the structure of local quantum states in finite-dimensional quantum systems, revealing a deep link between spacetime symmetries and quantum states.

## Contribution

It establishes a canonical derivation of local Lorentz covariance from three minimal postulates about local observable algebras and thermal states in Local Quantum Physics.

## Key findings

- Local Lorentz covariance arises from local quantum states.
- Vacuum restrictions determine local inertial frame connections.
- New relation between spacetime structure and quantum states.

## Abstract

We show that local Lorentz covariance arises canonically as the group of transformations between local thermal states in the framework of Local Quantum Physics, given the following three postulates: (i) Local observable algebras are finite-dimensional. (ii) Minimal local observable algebras are isomorphic to $\mathbb{M}_2(\mathbb{C})$, the observable algebra of a single qubit. (iii) The vacuum restricted to any minimal local observable algebra is a non-maximally mixed thermal state. The derivation reveals a new and surprising relation between spacetime structure and local quantum states. In particular, we show how local restrictions of the vacuum can determine the connection between different local inertial reference frames.