Systems with Quantum Dimensions

TL;DR

This paper introduces a novel framework where the number of spatial dimensions in a quantum system is treated as a quantum variable, leading to state-dependent dimensions and enhanced symmetries, with potential applications across physics.

Contribution

It presents a new approach to modeling systems with a quantum variable for spatial dimensions, including explicit analysis of a two-state system and its temperature-dependent effective dimension.

Findings

Effective dimension varies with temperature

Enhanced symmetries in quantum-dimension systems

Framework applicable to gravity and condensed matter

Abstract

We propose quantum-mechanical systems in which the number of spatial dimensions is promoted to a dynamical quantum variable, making the effective dimension state-dependent. Interestingly, systems of this form can exhibit enhanced symmetries compared to their fixed-dimensional counterparts. As an explicit example, we analyze a two-state system for which the number of spatial dimensions is represented by a quantum operator. By evaluating the corresponding partition function, we uncover a temperature-dependent effective dimension. Our framework opens a new avenue for constructing physical systems, from gravity to condensed matter, where the very notion of dimensionality becomes quantum.