- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Affine symmetry and the group-theoretic basis of the Unruh effect

Michele Arzano1,2,*, Alessandra D’Alise2,†, Simone del Rosso1,‡, and Domenico Frattulillo2,§

  • *Contact author: michele.arzano@na.infn.it
  • †Contact author: alessandra.dalise@na.infn.it
  • ‡Contact author: s.delrosso@studenti.unina.it
  • §Contact author: domenico.frattulillo@na.infn.it
PDF

Phys. Rev. D 113, 105009 – Published 13 May, 2026

DOI: https://doi.org/10.1103/696t-bzrp

Abstract

A massless scalar field in two spacetime dimensions splits into two independent sectors of left- and right-moving modes on the light cone. At the quantum level, these two sectors carry a representation of the group of affine transformations of the real line, with translations corresponding to transformations generated by light-cone momenta and dilations given by light-cone Rindler momenta formed by a linear combination of generators of boosts and dilations. One-particle states for inertial observers are eigenvectors of translation generators belonging to irreducible representations of the affine group. Rindler one-particle states are related to eigenfunctions of the generator of dilations. We show that simple manipulations connecting these two representations involving the Mellin transform can be used to derive the thermal spectrum of Rindler particles observed by an accelerated observer. Beyond providing a representation-theoretic basis for vacuum thermal effects, our results suggest that analogous phenomena may arise in any quantum system admitting realizations of translation and dilation eigenstates.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (30)

  1. W. G. Unruh, Phys. Rev. D 14, 870 (1976).
  2. S. A. Fulling, Phys. Rev. D 7, 2850 (1973).
  3. A. Ashtekar and A. Magnon, Proc. R. Soc. A 346, 375 (1975).
  4. S. W. Hawking, Commun. Math. Phys. 43, 199 (1975); 46, 206(E) (1976).
  5. G. W. Gibbons and S. W. Hawking, Phys. Rev. D 15, 2738 (1977).
  6. T. Jacobson, Phys. Rev. Lett. 75, 1260 (1995).
  7. T. Jacobson, Phys. Rev. Lett. 116, 201101 (2016).
  8. A. Svesko, Phys. Rev. D 99, 086006 (2019).
  9. A. Alonso-Serrano and M. Liška, Phys. Rev. D 102, 104056 (2020).
  10. P. Dorau and A. Much, Phys. Rev. Lett. 136, 091602 (2026).
  11. L. C. B. Crispino, A. Higuchi, and G. E. A. Matsas, Rev. Mod. Phys. 80, 787 (2008).
  12. J. F. Donoghue and B. R. Holstein, Am. J. Phys. 52, 730 (1984).
  13. S. Takagi, Prog. Theor. Phys. Suppl. 88, 1 (1986).
  14. J. Louko and A. Satz, Classical Quantum Gravity 23, 6321 (2006).
  15. S. M. Christensen and M. J. Duff, Nucl. Phys. B146, 11 (1978).
  16. K. Rajeev and T. Padmanabhan, J. Math. Phys. (N.Y.) 61, 062302 (2020).
  17. G. L. Sewell, Ann. Phys. (Amsterdam) 141, 201 (1982).
  18. B. S. Kay and R. M. Wald, Phys. Rep. 207, 49 (1991).
  19. J. Sorce, J. High Energy Phys. 24 (2024) 040.
  20. R. Kerner and R. B. Mann, Phys. Rev. D 73, 104010 (2006).
  21. R. M. Wald, Quantum Field Theory in Curved Space-Time and Black Hole Thermodynamics, Chicago Lectures in Physics (University of Chicago Press, Chicago, 1995), ISBN [Amazon][WorldCat].
  22. M. Arzano, A. D’Alise, and D. Frattulillo, Proc. Sci. CORFU2023 (2024) 276 [arXiv:2405.02623].
  23. I. Y. Aref’eva and I. V. Volovich, arXiv:1302.6699.
  24. M. Arzano and J. Kowalski-Glikman, Phys. Lett. B 788, 82 (2019).
  25. A. M. Zeitlin, Proc. Symp. Pure Math. 92, 325 (2016).
  26. N. J. Vilenkin, N. Vilenkin, N. Vilenkin, N. Vilenkin, N. Vilenkin, and V. Singh, Special Functions and the Theory of Group Representations, Translations of mathematical monographs (American Mathematical Society, Providence, 1968), ISBN [Amazon][WorldCat].
  27. R. Raczka and A. Barut, Theory of Group Representations and Applications (World Scientific Publishing Company, Singapore, 1986), ISBN [Amazon][WorldCat].
  28. M. Arzano and J. Kowalski-Glikman, Phys. Lett. B 788, 82 (2019).
  29. M. Arzano, Proc. Sci. CORFU2019 (2020) 227 [2003.14083].
  30. H. E. Moses and A. F. Quesada, Arch. Ration. Mech. Anal. 44, 217 (1972).

Outline

Information

Phys. Rev. D 113, 105009– Published 13 May, 2026
  • Received 20 January 2026
  • Accepted 17 April 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation