Operator Ordering in the Relativistic Quantization: Specific Heat in the Rindler Frame

• URL: http://arxiv.org/abs/2506.17362v2
• Date: Wed, 23 Jul 2025 22:02:19 GMT
• Title: Operator Ordering in the Relativistic Quantization: Specific Heat in the Rindler Frame
• Authors: Karol Sajnok, Kacper Dębski,
• Abstract summary: We introduce a covariant canonical quantization for a particle in curved spacetime that tracks operator-ordering ambiguities.<n>We derive a Hermitian Hamiltonian with leading quantum-relativistic corrections.<n> Numerical studies for electrons in extreme electric fields and ultra-light particles in strong gravitational fields demonstrate that these corrections become significant at intermediate temperatures.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a covariant canonical quantization for a particle in curved spacetime that tracks operator-ordering ambiguities. Parameterizing spatial and temporal ordering, we derive a Hermitian Hamiltonian with leading quantum-relativistic corrections. In a uniformly accelerated frame, we show the semiclassical heat-capacity approximation misses these effects and then develop a perturbative quantum treatment using Airy-function modes to obtain analytical first- and second-order energy shifts. Including these shifts in the partition function yields nontrivial, ordering-dependent specific-heat corrections. Numerical studies for electrons in extreme electric fields and ultra-light particles in strong gravitational fields demonstrate that these corrections become significant at intermediate temperatures. Enforcing the Tolman-Ehrenfest relation for spatial temperature variation further modulates the heat-capacity profile. Our results suggest that precision calorimetry in laser-acceleration or analogue gravity setups could probe quantum-ordering effects in relativistic regimes.

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