Momentum-Resolved Probing of Lorentz-Violating Dispersion Relations via Unruh-DeWitt Detector

Inspired by quantum gravity frameworks predicting Planck-scale deviations from Lorentz invariance, we probe Lorentz symmetry violation via modified dispersion relations $ω_{|\textbf{k}|}$. Departing from conventional approaches, we employ an Unruh-DeWitt detector to probe energy-dependent modifications to the dispersion relations. Two key methodological advances are introduced: (i) a generalized formulation for detector acceleration without assuming specific dispersion relations, and (ii) a momentum-resolved detection paradigm enabling spectral decomposition of $ω_{|\textbf{k}|}$ through localized momentum-shell integration. Analysis of deviations reveals disruption of the thermal spectrum under significant departures from the Lorentz invariance, while small perturbative regimes manifest as phase-modulated thermal distributions. By restricting detector-field interactions to narrow spectral windows and performing iterative Taylor expansions around reference momenta $|\textbf{k}_0|$, we derive coefficients encoding derivatives of $ω_{|\textbf{k}|}$, reconstructing its global profile via momentum-space tomography. Our approach offers a scalable method to test Lorentz symmetry violation across energy scales, and establishes a foundation for experimental verification of Planck-scale relics through high-precision spectral measurements.