scholarly journals Lorentz Violation at the Level of Undergraduate Classical Mechanics

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1734 ◽  
Author(s):  
Madeline Clyburn ◽  
Charles D. Lane
Keyword(s):  
Classical Limit ◽  
Binary Star ◽  
Equations Of Motion ◽  
Computational Simulation ◽  
Classical Mechanics ◽  
Lorentz Violation ◽  
Standard Model Extension ◽  
Model Extension ◽  
Binary Star System ◽  
Interesting Behavior

In this paper, we use the classical limit of the Standard-Model Extension to explore some generic features of Lorentz violation. This classical limit is formulated at the level of undergraduate physics. We first discuss the general equations of motion and then concentrate on three specific systems. First, we consider the theoretical aspects of pendulum motion in the presence of Lorentz violation, followed by some sample experimental results. The experimental bounds we achieve, in the range of 10−3, are not competitive with the current bounds from atomic clocks; rather, our experiment illustrates some common ideas and methods that appear in Lorentz-violation studies. We then discuss how Newton’s 2nd Law must be treated with caution in our model. Finally, we introduce a computational simulation of a binary star system that is perturbed by Lorentz-violating effects. This simulation shows some interesting behavior that could be the subject of future analytical studies.

scholarly journals Lorentz Violation of the Photon Sector in Field Theory Models

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Lingli Zhou ◽  
Bo-Qiang Ma
Keyword(s):  
Field Theory ◽  
Standard Model ◽  
Degrees Of Freedom ◽  
Lorentz Violation ◽  
Detailed Structure ◽  
Standard Model Extension ◽  
Model Extension ◽  
The Standard Model ◽  
Minimal Standard

We compare the Lorentz violation terms of the pure photon sector between two field theory models, namely, the minimal standard model extension (SME) and the standard model supplement (SMS). From the requirement of the identity of the intersection for the two models, we find that the free photon sector of the SMS can be a subset of the photon sector of the minimal SME. We not only obtain some relations between the SME parameters but also get some constraints on the SMS parameters from the SME parameters. The CPT-odd coefficients(kAF)αof the SME are predicted to be zero. There are 15 degrees of freedom in the Lorentz violation matrixΔαβof free photons of the SMS related with the same number of degrees of freedom in the tensor coefficients(kF)αβμν, which are independent from each other in the minimal SME but are interrelated in the intersection of the SMS and the minimal SME. With the related degrees of freedom, we obtain the conservative constraints(2σ)on the elements of the photon Lorentz violation matrix. The detailed structure of the photon Lorentz violation matrix suggests some applications to the Lorentz violation experiments for photons.

scholarly journals Formal Developments for Lorentz-Violating Dirac Fermions and Neutrinos

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1197
Author(s):  
João Alfíeres Andrade de Simões dos Reis ◽  
Marco Schreck
Keyword(s):  
Dispersion Equation ◽  
Lorentz Violation ◽  
Field Operator ◽  
Dirac Fermions ◽  
Dirac Theory ◽  
Standard Model Extension ◽  
Phenomenological Studies ◽  
Model Extension ◽  
The Matrix ◽  
Majorana Neutrinos

The current paper is a technical work that is focused on Lorentz violation for Dirac fermions as well as neutrinos, described within the nonminimal Standard-Model Extension. We intend to derive two theoretical results. The first is the full propagator of the single-fermion Dirac theory modified by Lorentz violation. The second is the dispersion equation for a theory of N neutrino flavors that enables the description of both Dirac and Majorana neutrinos. As the matrix structure of the neutrino field operator is very involved for generic N, we will use sophisticated methods of linear algebra to achieve our objectives. Our main finding is that the neutrino dispersion equation has the same structure in terms of Lorentz-violating operators as that of a modified single-fermion Dirac theory. The results will be valuable for phenomenological studies of Lorentz-violating Dirac fermions and neutrinos.

scholarly journals Effects of Lorentz violation through the γe → Wνe process in the Standard Model extension

2014 ◽  
Vol 41 (5) ◽  
pp. 055003 ◽  
Author(s):  
J I Aranda ◽  
F Ramírez-Zavaleta ◽  
D A Rosete ◽  
F J Tlachino ◽  
J J Toscano ◽  
...  
Keyword(s):  
Standard Model ◽  
Lorentz Violation ◽  
Standard Model Extension ◽  
Model Extension ◽  
The Standard Model

scholarly journals One-loop nonbirefringent effects on the electromagnetic vertex in the Standard Model Extension

2014 ◽  
Vol 29 (22) ◽  
pp. 1450107 ◽  
Author(s):  
A. Moyotl ◽  
H. Novales-Sanchez ◽  
J. J. Toscano ◽  
E. S. Tututi
Keyword(s):  
Standard Model ◽  
Lorentz Invariance ◽  
Lorentz Violation ◽  
Tree Level ◽  
Isotropic Case ◽  
Photon Propagator ◽  
Standard Model Extension ◽  
Model Extension ◽  
The One ◽  
Electromagnetic Vertex

Lorentz violation emerged from a fundamental description of nature may impact, at low energies, the Maxwell sector, so that contributions from such new physics to the electromagnetic vertex would be induced. Particularly, nonbirefringent CPT-even effects from the electromagnetic sector modified by the Lorentz- and CPT-violating Standard Model Extension alter the structure of the free photon propagator. We calculate Lorentz-violating contributions to the electromagnetic vertex, at the one-loop level, by using a modified photon propagator carrying this sort of effects. We take the photon off shell, and find an expression that involves both isotropic and anisotropic effects of nonbirefringent violation of Lorentz invariance. Our analysis of the one-loop vertex function includes gauge invariance, transformation properties under C, P and T, and tree-level contributions from Lorentz-violating nonrenormalizable interactions. These elements add to previous studies of the one-loop contributions to the electromagnetic vertex in the context of Lorentz violation in the photon sector. Finally, we restrict our analysis to the isotropic case and derive a finite contribution from isotropic Lorentz violation to the anomalous magnetic moment of fermions that coincides with the result already reported in the literature.

scholarly journals UNDERSTANDING LORENTZ VIOLATION WITH RASHBA INTERACTION

2012 ◽  
Vol 27 (24) ◽  
pp. 1250139 ◽  
Author(s):  
MUHAMMAD ADEEL AJAIB
Keyword(s):  
Condensed Matter ◽  
Lorentz Violation ◽  
Condensed Matter Physics ◽  
Coupling Constant ◽  
Standard Model Extension ◽  
Rashba Interaction ◽  
Model Extension ◽  
The Standard Model ◽  
Spatial Dimensions ◽  
Rashba Coupling

Rashba spin–orbit interaction is a well-studied effect in condensed matter physics and has important applications in spintronics. The standard model extension (SME) includes a CPT-even term with the coefficient Hμν, which leads to the Rashba interaction term. From the limit available on the coefficient Hμν in the SME we derive a limit on the Rashba coupling constant for Lorentz violation. In condensed matter physics the Rashba term is understood as resulting from an asymmetry in the confining potential at the interface of two different types of semiconductors. Based on this interpretation we suggest that a possible way of inducing the Hμν term in the SME is with an asymmetry in the potential that confines us to three spatial dimensions.

scholarly journals NEW CHANCE FOR RESEARCHES ON LORENTZ VIOLATION

2012 ◽  
Vol 10 ◽  
pp. 195-206 ◽  
Author(s):  
BO-QIANG MA
Keyword(s):  
Field Theory ◽  
Standard Model ◽  
Effective Field Theory ◽  
Lorentz Violation ◽  
Phenomenological Analysis ◽  
Effective Field ◽  
Standard Model Extension ◽  
Model Extension ◽  
The Standard Model

I present a brief review on the motivation for the study on Lorentz violation and on some of our studies with phenomenological analysis of Lorentz violation effects. I also discuss three effective field theory frameworks for Lorentz violation: the Coleman-Glashow model, the standard model extension (SME), and the standard model supplement (SMS). The situation of the OPERA "anomaly" is also briefly reviewed, together with some discussion on the superluminality of neutrinos within the effective field theory frameworks.

scholarly journals LORENTZ VIOLATION DISPERSION RELATION AND ITS APPLICATION

2009 ◽  
Vol 24 (07) ◽  
pp. 1359-1381 ◽  
Author(s):  
ZHI XIAO ◽  
BO-QIANG MA
Keyword(s):  
Dispersion Relation ◽  
Quantum Electrodynamics ◽  
Lorentz Violation ◽  
Cosmic Ray ◽  
Ultrahigh Energy ◽  
Standard Model Extension ◽  
Modified Dispersion Relation ◽  
Model Extension ◽  
The Standard Model ◽  
Spinor Formalism

We derive a modified dispersion relation (MDR) in the Lorentz violation extension of the quantum electrodynamics (QED) sector in the standard model extension (SME) framework. Based on the extended Dirac equation and corresponding MDR, we observe the resemblance of the Lorentz violation coupling to spin–gravity coupling. We also develop a neutrino oscillation mechanism induced by the presence of nondiagonal terms of Lorentz violation couplings in two-flavor space in a two-spinor formalism by explicitly assuming neutrinos to be Marjorana fermions. We also obtain a very stringent bound (∽ 10-25) on one of the Lorentz violation parameters by applying the MDR to the ultrahigh energy cosmic ray (UHECR) problem.

scholarly journals (Gravitational) Vacuum Cherenkov Radiation

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 424 ◽  
Author(s):  
Marco Schreck
Keyword(s):  
Cherenkov Radiation ◽  
Lorentz Invariance ◽  
Lorentz Violation ◽  
Minkowski Spacetime ◽  
Standard Model Extension ◽  
Essential Properties ◽  
Model Extension ◽  
The Standard Model ◽  
Gravitational Vacuum ◽  
The Common

This work reviews our current understanding of Cherenkov-type processes in vacuum that may occur due to a possible violation of Lorentz invariance. The description of Lorentz violation is based on the Standard Model Extension (SME). To get an overview as general as possible, the most important findings for vacuum Cherenkov radiation in Minkowski spacetime are discussed. After doing so, special emphasis is put on gravitational Cherenkov radiation. For a better understanding, the essential properties of the gravitational SME are recalled in this context. The common grounds and differences of vacuum Cherenkov radiation in Minkowski spacetime and in the gravity sector are emphasized.

An effective theory with Lorentz violation and minimum length

2018 ◽  
Vol 27 (11) ◽  
pp. 1843006 ◽  
Author(s):  
E. V. B. Leite ◽  
H. Belich
Keyword(s):  
Lorentz Violation ◽  
Heisenberg Algebra ◽  
Effective Theory ◽  
Minimum Length ◽  
Standard Model Extension ◽  
Gauge Sector ◽  
Model Extension ◽  
Symmetry Breaking Term ◽  
Lorentz Symmetry Breaking ◽  
Breaking Term

We have made an initial investigation of an effective theory with Lorentz violation with Minimum Length. We investigate a scenario of anisotropy generated by a Lorentz symmetry breaking term which appears in Standard Model Extension (SME) on the even gauge sector with deformed Heisenberg algebra associated to the Minimum Length (ML). To study such possible correction of the gauge sector of SME, we analyze the dispersion relations of this model.

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