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arXiv · 2511.14547

Systems with Quantum Dimensions

Mikołaj Myszkowski·Mattia Damia Paciarini·Francesco Sannino
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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.

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Mikołaj Myszkowski, Mattia Damia Paciarini, Francesco Sannino. 2025-11-18. Systems with Quantum Dimensions. https://arxiv.org/abs/2511.14547

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