Systems with Quantum Dimensions

• URL: http://arxiv.org/abs/2511.14547v1
• Date: Tue, 18 Nov 2025 14:50:49 GMT
• Title: Systems with Quantum Dimensions
• Authors: Mikołaj Myszkowski, Mattia Damia Paciarini, Francesco Sannino,
• Abstract summary: We propose quantum-mechanical systems in which the number of spatial dimensions is promoted to a dynamical quantum variable.<n>Our framework opens a new avenue for constructing physical systems, from gravity to condensed matter, where the very notion of dimensionality becomes quantum.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose quantum-mechanical systems in which the number of spatial dimensions is promoted to a dynamical quantum variable. As a consequence, the effective dimension depends on the physical state of the system. Interestingly, systems of this form exhibit enhanced symmetries compared to their fixed-dimensional counterparts. As an explicit example, we analyze a harmonic oscillator for which the spatial dimension 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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