Quantum degrees of freedom of a region of spacetime

TL;DR

This paper explores the nature of quantum degrees of freedom in finite regions of spacetime, proposing a new intrinsic way to define localized subsystems that aligns with holographic and thermodynamic principles.

Contribution

It introduces a novel approach to identify localized regions as subsystems based on the intrinsic dynamics of the quantum state, avoiding traditional point-based labeling.

Findings

Proposes a new method for defining localized quantum subsystems.

Addresses compatibility issues with Lorentz invariance and spacetime dynamics.

Suggests a framework consistent with holographic principles.

Abstract

The holographic principle and the thermodynamics of de Sitter space suggest that the total number of fundamental degrees of freedom associated with any finite-volume region of space may be finite. The naive picture of a short distance cut-off, however, is hardly compatible with the dynamical properties of spacetime, let alone with Lorentz invariance. Considering the regions of space just as general ``subsystems'' may help clarifying this problem. In usual QFT the regions of space are, in fact, associated with a tensor product decomposition of the total Hilbert space into ``subsystems'', but such a decomposition is given a priori and the fundamental degrees of freedom are labelled, already from the beginning, by the spacetime points. We suggest a new strategy to identify ``localized regions'' as ``subsystems'' in a way which is intrinsic to the total Hilbert-space dynamics of the quantum state of the fields.