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Description
How do quantum systems behave in a gravitational field, and what role does operator ordering play in their quantization? This work presents a consistent framework for relativistic quantization, tackling the longstanding operator ordering problem through the introduction of arbitrary constants and by coupling internal quantum and external gravitational degrees of freedom. A general, relativistically invariant Hamiltonian is derived, capturing leading-order quantum and relativistic corrections, and allowing for operator ordering parameters that may be probed experimentally. Using perturbation theory, we compute the corrected energy spectrum and apply it to evaluate thermodynamic properties, focusing on the specific heat of a bosonic gas in Rindler coordinates. The resulting relativistic quantum corrections to specific heat could be accessible in state-of-the-art setups, such as counterpropagating laser traps generating strong accelerations. These findings offer a realistic path toward testing gravitational quantum effects through thermodynamic observables.
