Relativistic Dispersion Spectra across Lorentz boosted frames: Spurious modes and the enigma of causality
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913158655901696 |
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| author | Bhattacharyya, Sayantani Mitra, Sukanya Roy, Shuvayu Singh, Rajeev |
| author_facet | Bhattacharyya, Sayantani Mitra, Sukanya Roy, Shuvayu Singh, Rajeev |
| contents | The analysis of excitation spectra in gradient-expanded relativistic fluid theories frequently leads to pathologies under Lorentz boosts. However, extracting the dispersion modes in a Lorentz boosted inertial frame can be nontrivial. Motivated by this problem, we develop a general framework for deriving the linearized dispersion spectra in Lorentz boosted frames using only information from the local rest-frame dispersion structure, particularly its mode-expansion coefficients. We observe that, under a Lorentz transformation from the local rest frame, additional boosted solutions may appear that conflict with the causality of the theory; we refer to these as "spurious modes." The key developments presented here are: (i) a convenient method for obtaining dispersion spectra across inertial frames, bypassing the traditional procedure of solving the boosted polynomial, and (ii) the establishment of a direct connection between mode conservation and the causality of a theory, supported by a detailed proof. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12450 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Relativistic Dispersion Spectra across Lorentz boosted frames: Spurious modes and the enigma of causality Bhattacharyya, Sayantani Mitra, Sukanya Roy, Shuvayu Singh, Rajeev High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Phenomenology Nuclear Theory The analysis of excitation spectra in gradient-expanded relativistic fluid theories frequently leads to pathologies under Lorentz boosts. However, extracting the dispersion modes in a Lorentz boosted inertial frame can be nontrivial. Motivated by this problem, we develop a general framework for deriving the linearized dispersion spectra in Lorentz boosted frames using only information from the local rest-frame dispersion structure, particularly its mode-expansion coefficients. We observe that, under a Lorentz transformation from the local rest frame, additional boosted solutions may appear that conflict with the causality of the theory; we refer to these as "spurious modes." The key developments presented here are: (i) a convenient method for obtaining dispersion spectra across inertial frames, bypassing the traditional procedure of solving the boosted polynomial, and (ii) the establishment of a direct connection between mode conservation and the causality of a theory, supported by a detailed proof. |
| title | Relativistic Dispersion Spectra across Lorentz boosted frames: Spurious modes and the enigma of causality |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Phenomenology Nuclear Theory |
| url | https://arxiv.org/abs/2512.12450 |