Quantum Reference Frames and Correlation Geometry

TL;DR

This paper introduces correlation geometry within the causal fermion system framework, emphasizing gauge invariance and drawing conceptual parallels to thermodynamics rather than quantum theory.

Contribution

It provides a self-contained introduction to correlation geometry and explores its relation to gauge transformations and thermodynamic concepts.

Findings

Correlation geometry underpins the causal fermion system theory.

Gauge transformations are handled via unitary equivalence.

The framework aligns more closely with thermodynamics than quantum mechanics.

Abstract

The aim of this paper is to provide a largely self-contained, compact and comprehensible introduction to the basic ideas behind correlation geometry, which underlies the theory of causal fermion system (CFS). A key focus here is on the manner in which the framework deals with gauge transformations, including diffeomorphisms via the principle of unitary equivalence. We will argue that, conceptually, the fundamental description of a physical system in terms of its correlation geometry is much closer to thermodynamics than quantum theory.