Lorentz Invariance Violation and Space–Time Symmetry Breaking

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: 31 December 2025 | Viewed by 1938

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Guest Editor
School of Physics, Peking University, Beijing 100871, China
Interests: particle physics and astroparticle physics
Special Issues, Collections and Topics in MDPI journals
School of Physics, Peking University, Beijing 100871, China
Interests: space-time symmetry; string phenomenology; astroparticle physics; new physics

Special Issue Information

Dear Colleagues,

Lorentz invariance is one of the fundamental principles of Einstein's relativity and quantum field theories. In most of the standard models of modern physics, it is assumed to be an exact symmetry that should be preserved at all scales. This idea is supported by a lot of remarkably precise Earth-based laboratory experiments, with no violations detected to date. However, there are many new models of physics beyond the standard model with various interesting mechanisms, some of which, especially quantum gravity (QG) theories, have provoked a violation of Lorentz invariance. In these models, the effects arising from the microscopic fabric of space–time are expected to appear at distances of the order of the Planck length. For more than 30 years, studies unraveling the nature of quantum gravity/space–time through violations of Lorentz (LV) and charge-parity-time symmetry (CPTV) have attracted significant attention from both theoretical and phenomenological perspectives, given that they can provide intriguing hints at physics beyond relativity, and may eventually allow a breakthrough paradigm shift from our current understanding of the fundamental structure of space–time. In terms of theoretical work, different types of effective theories of QG have been explored to investigate the origin and the consequence of these symmetry violations. These include low-energy effective field theory models, bottom-up scenarios, such as doubly special relativity, and top-down methods involving non-local stringy or membrane-like objects that naturally include the graviton as an ingredient, or a loop approach to canonical quantum gravity. Different theories yield quite distinct phenomenological predictions. Delays in the time of flight of massless particles, e.g.,  photons or ultrarelativistic neutrinos, can be a signature for almost all of them. However, other constraints, such as modification or appearance of reaction thresholds, or birefringence effects, do not apply in the same way. On the experimental side, this leads to the establishment of constraints for high-energy LVs in dispersion relations for different particles through astrophysical observations. From the phenomenological side, this leads to new possible theoretical interpretations regarding the potential of finding authentic signatures for quantum gravity from experiments.

This Special Issue is devoted to both the presentation of new results on the observational constraints on LV and CPTV (and, presumably, on the underlying QG), and the overview of theoretical and experimental aspects of space–time symmetry breaking and departures from CPT and Lorentz invariance, involving at least: quantum field theory and gravitation, particle (astro)physics, phenomenologies of theories beyond the standard model, origins and mechanisms of Lorentz and/or CPT violation, and Finsler geometry and its mathematical foundations.

Prof. Dr. Bo-Qiang Ma
Dr. Chengyi Li
Guest Editors

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Keywords

  • Lorentz invariance violation
  • CPT symmetry violation
  • spontaneous symmetry breaking
  • space–time symmetries
  • quantum gravity
  • phenomenology of physics beyond the standard model
  • astroparticle physics and cosmology
  • test of Einstein's relativity

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Published Papers (2 papers)

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Research

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18 pages, 354 KiB  
Article
Testing the Universality of Quantum Gravity Theories with Cosmic Messengers in the Context of DSR Theories
by Marco Danilo Claudio Torri
Symmetry 2025, 17(2), 203; https://doi.org/10.3390/sym17020203 - 28 Jan 2025
Viewed by 532
Abstract
Recently there have been several studies devoted to the investigation of the fate of fundamental relativistic symmetries at the foreseen unification of gravity and quantum regime, that is the Planck scale. In order to preserve covariance of the formulation even if in an [...] Read more.
Recently there have been several studies devoted to the investigation of the fate of fundamental relativistic symmetries at the foreseen unification of gravity and quantum regime, that is the Planck scale. In order to preserve covariance of the formulation even if in an amended formulation, new mathematical tools are required. In this work, we consider DSR theories that modify covariance by introducing a non-trivial structure in momentum space. Additionally, we explore the possibility of investigating both universal quantum gravity corrections and scenarios where different particle species are corrected differently within the framework of these models. Several astroparticle phenomena are then analyzed to test the phenomenological predictions of DSR models. Full article
(This article belongs to the Special Issue Lorentz Invariance Violation and Space–Time Symmetry Breaking)
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Review

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46 pages, 700 KiB  
Review
Probes for String-Inspired Foam, Lorentz, and CPT Violations in Astrophysics
by Chengyi Li and Bo-Qiang Ma
Symmetry 2025, 17(6), 974; https://doi.org/10.3390/sym17060974 - 19 Jun 2025
Viewed by 384
Abstract
Lorentz invariance is such a basic principle in fundamental physics that it must be constantly tested and any proposal of its violation and breakdown of CPT symmetry that might characterize some approaches to quantum gravity should be treated with care. In this review, [...] Read more.
Lorentz invariance is such a basic principle in fundamental physics that it must be constantly tested and any proposal of its violation and breakdown of CPT symmetry that might characterize some approaches to quantum gravity should be treated with care. In this review, we examine, among other scenarios, such instances in supercritical (Liouville) string theory, particularly in some brane models for “quantum foam”. Using the phenomenological formalism introduced here, we analyze the observational hints of Lorentz violation in time-of-flight lags of cosmic photons and neutrinos which fit excellently stringy space–time foam scenarios. We further demonstrate how stringent constraints from other astrophysical data, including the recent first detections of multi-TeV events in γ-ray burst 221009A and PeV cosmic photons by the Large High Altitude Air Shower Observatory (LHAASO), are satisfied in this context. Such models thus provide a unified framework for all currently observed phenomenologies of space–time symmetry breaking at Planckian scales. Full article
(This article belongs to the Special Issue Lorentz Invariance Violation and Space–Time Symmetry Breaking)
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