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Symmetry
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Space-Time Symmetries and Violations of Lorentz Invariance
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Space-Time Symmetries and Violations of Lorentz Invariance

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

Deadline for manuscript submissions: closed (31 August 2021) | Viewed by 13723

Special Issue Editor

Dr. Matthew Mewes

E-Mail Website
Guest Editor
Department of Physics, California Polytechnic State University, San Luis Obispo, CA, USA
Interests: particle physics; lorentz violation

Special Issue Information

Lorentz invariance is a foundational principle of both the Standard Model of particle physics and of general relativity. However, attempts to reconcile gravity and quantum mechanics suggest Lorentz symmetry may be violated at low energies. Remarkably, minuscule Lorentz violations with roots in Planck-scale physics could be within the experimental reach of current technology. Consequently, violations of Lorentz invariance and the related CPT invariance provide a promising area for discovery.

Recent decades have seen a surge of interest in testing Lorentz and CPT symmetries. A steady progression on the theoretical front has yielded a vast landscape of potential Lorentz and CPT violations. Meanwhile, hundreds of high-precision tests of Lorentz and CPT invariance in a wide range of systems have been performed. These include laboratory experiments involving atoms and photons, studies of high-energy particles from accelerators and the cosmos, observations of photons, neutrinos, and gravitational waves from astrophysical sources, and tests of gravity in the laboratory and in space. This Special Issue explores all aspects of this exciting and growing field.

Dr. Matthew Mewes
Guest Editor

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Keywords

  • space–time symmetry
  • Lorentz invariance
  • Lorentz violation
  • CPT
  • tests of relativity
  • Standard Model extension

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Published Papers (7 papers)

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Research

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20 pages, 344 KiB  
Article
The Axial Anomaly in Lorentz Violating Theories: Towards the Electromagnetic Response of Weakly Tilted Weyl Semimetals
by Andrés Gómez and Luis Urrutia
Symmetry 2021, 13(7), 1181; https://doi.org/10.3390/sym13071181 - 30 Jun 2021
Cited by 4 | Viewed by 1648
Abstract
Using the path integral formulation in Euclidean space, we extended the calculation of the abelian chiral anomalies in the case of Lorentz violating theories by considering a new fermionic correction term provided by the standard model extension, which arises in the continuous Hamiltonian [...] Read more.
Using the path integral formulation in Euclidean space, we extended the calculation of the abelian chiral anomalies in the case of Lorentz violating theories by considering a new fermionic correction term provided by the standard model extension, which arises in the continuous Hamiltonian of a weakly tilted Weyl semimetal, and whose cones have opposite tilting. We found that this anomaly is insensitive to the tilting parameter, retaining its well-known covariant form. This independence on the Lorentz violating parameters is consistent with other findings reported in the literature. The initially imposed gauge invariant regularization was consistently recovered at the end of the calculation by the appearance of highly non-trivial combinations of the covariant derivatives, which ultimately managed to give only terms containing the electromagnetic tensor. We emphasize that the value of the anomaly with an arbitrary parameter is not automatically related to the effective action describing the electromagnetic response of such materials. Full article
(This article belongs to the Special Issue Space-Time Symmetries and Violations of Lorentz Invariance)
22 pages, 509 KiB  
Article
New Constraints on Lorentz Invariance Violation from Combined Linear and Circular Optical Polarimetry of Extragalactic Sources
by Roman Gerasimov, Praneet Bhoj and Fabian Kislat
Symmetry 2021, 13(5), 880; https://doi.org/10.3390/sym13050880 - 15 May 2021
Cited by 6 | Viewed by 2073
Abstract
Expanding on our prior efforts to search for Lorentz invariance violation (LIV) using the linear optical polarimetry of extragalactic objects, we propose a new method that combines linear and circular polarization measurements. While existing work has focused on the tendency of LIV to [...] Read more.
Expanding on our prior efforts to search for Lorentz invariance violation (LIV) using the linear optical polarimetry of extragalactic objects, we propose a new method that combines linear and circular polarization measurements. While existing work has focused on the tendency of LIV to reduce the linear polarization degree, this new method additionally takes into account the coupling between photon helicities induced by some models. This coupling can generate circular polarization as light propagates, even if there is no circular polarization at the source. Combining significant detections of linear polarization of light from extragalactic objects with the absence of the detection of circular polarization in most measurements results in significantly tighter constraints regarding LIV. The analysis was carried out in the framework of the Standard-Model Extension (SME), an effective field theory framework to describe the low-energy effects of an underlying fundamental quantum gravity theory. We evaluate the performance of our method by deriving constraints on the mass dimension d=4 CPT-even SME coefficients from a small set of archival circular and linear optical polarimetry constraints and compare them to similar constraints derived in previous works with far larger sample sizes and based on linear polarimetry only. The new method yielded constraints that are an order of magnitude tighter even for our modest sample size of 21 objects. Based on the demonstrated gain in constraining power from scarce circular data, we advocate for the need for future extragalactic circular polarization surveys. Full article
(This article belongs to the Special Issue Space-Time Symmetries and Violations of Lorentz Invariance)
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11 pages, 283 KiB  
Article
Construction of Higher-Order Metric Fluctuation Terms in Spacetime Symmetry-Breaking Effective Field Theory
by Quentin G. Bailey
Symmetry 2021, 13(5), 834; https://doi.org/10.3390/sym13050834 - 10 May 2021
Cited by 6 | Viewed by 1411
Abstract
We examined the basic conservation laws for diffeomorphism symmetry in the context of spontaneous diffeomorphism and local Lorentz-symmetry breaking. The conservation laws were used as constraints on a generic series of terms in an expansion around a flat background. We found all such [...] Read more.
We examined the basic conservation laws for diffeomorphism symmetry in the context of spontaneous diffeomorphism and local Lorentz-symmetry breaking. The conservation laws were used as constraints on a generic series of terms in an expansion around a flat background. We found all such terms for a two-tensor coupling to cubic order in the metric and tensor field fluctuations. The results are presented in a form that can be used for phenomenological calculations. One key result is that if we preserve the underlying diffeomorphism symmetry in a spontaneous-symmetry breaking scenario, one cannot decouple the two-tensor fluctuations from the metric fluctuations at the level of the action, except in special cases of the quadratic actions. Full article
(This article belongs to the Special Issue Space-Time Symmetries and Violations of Lorentz Invariance)
10 pages, 269 KiB  
Article
Improved Bounds on Lorentz Symmetry Violation from High-Energy Astrophysical Sources
by Brett Altschul
Symmetry 2021, 13(4), 688; https://doi.org/10.3390/sym13040688 - 15 Apr 2021
Cited by 5 | Viewed by 1866
Abstract
Observations of the synchrotron and inverse Compton emissions from ultrarelativistic electrons in astrophysical sources can reveal a great deal about the energy–momentum relations of those electrons. They can thus be used to place bounds on the possibility of Lorentz violation in the electron [...] Read more.
Observations of the synchrotron and inverse Compton emissions from ultrarelativistic electrons in astrophysical sources can reveal a great deal about the energy–momentum relations of those electrons. They can thus be used to place bounds on the possibility of Lorentz violation in the electron sector. Recent γ-ray telescope data allow the Lorentz-violating electron cνμ parameters to be constrained extremely well, so that all bounds are at the level of 7×10−16 or better. Full article
(This article belongs to the Special Issue Space-Time Symmetries and Violations of Lorentz Invariance)
18 pages, 340 KiB  
Article
Gravity with Explicit Diffeomorphism Breaking
by Robert Bluhm and Yumu Yang
Symmetry 2021, 13(4), 660; https://doi.org/10.3390/sym13040660 - 12 Apr 2021
Cited by 10 | Viewed by 2143
Abstract
Modified theories of gravity that explicitly break diffeomorphism invariance have been used for over a decade to explore open issues related to quantum gravity, dark energy, and dark matter. At the same time, the Standard-Model Extension (SME) has been widely used as a [...] Read more.
Modified theories of gravity that explicitly break diffeomorphism invariance have been used for over a decade to explore open issues related to quantum gravity, dark energy, and dark matter. At the same time, the Standard-Model Extension (SME) has been widely used as a phenomenological framework in investigations of spacetime symmetry breaking. Until recently, it was thought that the SME was suitable only for theories with spontaneous spacetime symmetry breaking due to consistency conditions stemming from the Bianchi identities. However, it has recently been shown that, particularly with matter couplings included, the consistency conditions can also be satisfied in theories with explicit breaking. An overview of how this is achieved is presented, and two examples are examined. The first is massive gravity, which includes a nondynamical background tensor. The second is a model based on a low-energy limit of Hořava gravity, where spacetime has a physically preferred foliation. In both cases, bounds on matter–gravity interactions that explicitly break diffeomorphisms are obtained using the SME. Full article
(This article belongs to the Special Issue Space-Time Symmetries and Violations of Lorentz Invariance)
25 pages, 460 KiB  
Article
Non-Minimal Lorentz Violation in Macroscopic Matter
by Matthew Mewes
Symmetry 2020, 12(12), 2026; https://doi.org/10.3390/sym12122026 - 7 Dec 2020
Cited by 1 | Viewed by 1616
Abstract
The effects of Lorentz and CPT violations on macroscopic objects are explored. Effective composite coefficients for Lorentz violation are derived in terms of coefficients for electrons, protons, and neutrons in the Standard-Model Extension, including all minimal and non-minimal violations. The hamiltonian and modified [...] Read more.
The effects of Lorentz and CPT violations on macroscopic objects are explored. Effective composite coefficients for Lorentz violation are derived in terms of coefficients for electrons, protons, and neutrons in the Standard-Model Extension, including all minimal and non-minimal violations. The hamiltonian and modified Newton’s second law for a test body are derived. The framework is applied to free-fall and torsion-balance tests of the weak equivalence principle and to orbital motion. The effects on continuous media are studied, and the frequency shifts in acoustic resonators are calculated. Full article
(This article belongs to the Special Issue Space-Time Symmetries and Violations of Lorentz Invariance)
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Review

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20 pages, 363 KiB  
Review
Penning-Trap Searches for Lorentz and CPT Violation
by Yunhua Ding, Teague D. Olewiler and Mohammad Farhan Rawnak
Symmetry 2021, 13(9), 1703; https://doi.org/10.3390/sym13091703 - 15 Sep 2021
Cited by 2 | Viewed by 1632
Abstract
An overview of recent progress on testing Lorentz and CPT symmetry using Penning traps is presented. The theory of quantum electrodynamics with Lorentz-violating operators of mass dimensions up to six is summarized. Dominant shifts in the cyclotron and anomaly frequencies of the confined [...] Read more.
An overview of recent progress on testing Lorentz and CPT symmetry using Penning traps is presented. The theory of quantum electrodynamics with Lorentz-violating operators of mass dimensions up to six is summarized. Dominant shifts in the cyclotron and anomaly frequencies of the confined particles and antiparticles due to Lorentz and CPT violation are derived. Existing results of the comparisons of charge-to-mass ratios and magnetic moments involving protons, antiprotons, electrons, and positrons are used to constrain various coefficients for Lorentz violation. Full article
(This article belongs to the Special Issue Space-Time Symmetries and Violations of Lorentz Invariance)
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