Thermodynamics of relativistic oscillators coupled to a fuzzy-sphere internal spectrum
Abstract
We study the canonical thermodynamics of a one-particle model in which a relativistic oscillator in d spatial dimensions is coupled to the finite Laplacian spectrum of a fuzzy two-sphere with angular-momentum cutoff J F ; the fuzzy eigenvalues shift the squared mass. In the nonrelativistic window, where the partition function factorises, the internal heat capacity follows the known positive T − 2 finite-spectrum law. For the full Klein–Gordon trace at fixed finite J F and fixed model parameters, the fuzzy contribution to the heat capacity is instead negative and decays as T − 2 , with a mass- and dimension-dependent coefficient; its leading term and, for d ≥ 3, its next-to-leading term are derived and confirmed by exact canonical sums. The two T − 2 laws hold in disjoint regimes, because the corresponding limits do not commute. For the three-dimensional Dirac oscillator, the unrestricted canonical trace diverges; spinor results are therefore defined only in a conditional ensemble with fixed conserved total angular momentum, which does not regularise or replace the unrestricted trace. No large- J F or commutative limit is considered.
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BibTeX
@article{boumali2026thermodynamics,
title = {{Thermodynamics of relativistic oscillators coupled to a fuzzy-sphere internal spectrum}},
author = {Abdelmalek Boumali},
journal = {Nuclear Physics B},
year = {2026},
month = oct,
doi = {10.1016/j.nuclphysb.2026.117691},
url = {https://linkinghub.elsevier.com/retrieve/pii/S0550321326003949},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Thermodynamics of relativistic oscillators coupled to a fuzzy-sphere internal spectrum
AU - Abdelmalek Boumali
PY - 2026
DA - 2026/10/30
JO - Nuclear Physics B
DO - 10.1016/j.nuclphysb.2026.117691
UR - https://linkinghub.elsevier.com/retrieve/pii/S0550321326003949
AB - We study the canonical thermodynamics of a one-particle model in which a relativistic oscillator in d spatial dimensions is coupled to the finite Laplacian spectrum of a fuzzy two-sphere with angular-momentum cutoff J F ; the fuzzy eigenvalues shift the squared mass. In the nonrelativistic window, where the partition function factorises, the internal heat capacity follows the known positive T − 2 finite-spectrum law. For the full Klein–Gordon trace at fixed finite J F and fixed model parameters, the fuzzy contribution to the heat capacity is instead negative and decays as T − 2 , with a mass- and dimension-dependent coefficient; its leading term and, for d ≥ 3, its next-to-leading term are derived and confirmed by exact canonical sums. The two T − 2 laws hold in disjoint regimes, because the corresponding limits do not commute. For the three-dimensional Dirac oscillator, the unrestricted canonical trace diverges; spinor results are therefore defined only in a conditional ensemble with fixed conserved total angular momentum, which does not regularise or replace the unrestricted trace. No large- J F or commutative limit is considered.
SN - 0550-3213
SN - 1873-1562
ER -