On the effects of rotation and violation of the Lorentz symmetry on the scalar field

2020 ◽  
Vol 35 (05) ◽  
pp. 2050023
Author(s):  
K. Bakke ◽  
H. Belich
Keyword(s):  
Scalar Field ◽  
Lorentz Symmetry ◽  
Point Of View ◽  
Radial Coordinate ◽  
Hard Wall ◽  
Confining Potential ◽  
Upper Limit ◽  
Minkowski Space Time ◽  
Effects Of Rotation ◽  
Line Elements

We deal with the effects of rotation and violation of the Lorentz symmetry on the scalar field from a geometrical point of view. By choosing a fixed spacelike four-vector and a fixed timelike four-vector, we obtain two modified line elements for the Minkowski space–time. In addition, we consider a uniformly rotating frame. Then, we analyze how the effects of rotation and violation of the Lorentz symmetry determine the upper limit of the radial coordinate. Further, we analyze the effects of rotation and violation of the Lorentz symmetry on the confinement of the scalar field to a hard-wall confining potential.

Effects of rotation on a scalar field in a Kaluza–Klein theory

2020 ◽  
Vol 35 (34) ◽  
pp. 2050283
Author(s):  
E. V. B. Leite ◽  
H. Belich ◽  
R. L. L. Vitória
Keyword(s):  
Scalar Field ◽  
Energy Levels ◽  
Scalar Particle ◽  
Point Of View ◽  
Relativistic Energy ◽  
Theoretical Point ◽  
Klein Theory ◽  
Klein Gordon ◽  
Effects Of Rotation ◽  
Kaluza Klein

We have investigated the effects of rotation on a scalar field subject to the Aharonov–Bohm effect, an effect arising from a particular and possible scenario, from the theoretical point of view, of the Kaluza–Klein theory. Through the boundary condition induced by the non-inertial effect, for a particular case, we analyze a scalar particle in a region bounded by the cylindrical surfaces and under the effects of a hard-wall confining potential. In addition, a scalar particle with position-dependent mass interacting with the Coulomb-type potential. Then, in this scenario of the Kaluza–Klein theory in a uniformly rotating frame, we analyze the Klein–Gordon oscillator. In all cases an effect analogous to the Sagnac effect is observed on the relativistic energy levels determined analytically.

DESITTER GAUGE THEORY OF GRAVITATION

2003 ◽  
Vol 14 (01) ◽  
pp. 41-48 ◽  
Author(s):  
G. ZET ◽  
V. MANTA ◽  
S. BABETI
Keyword(s):  
Gauge Theory ◽  
Riemann Tensor ◽  
Space Time ◽  
Point Of View ◽  
Field Equations ◽  
Minkowski Space Time ◽  
Strength Tensor ◽  
Group A ◽  
Theory Of Gravitation ◽  
Tensor Formula

A deSitter gauge theory of gravitation over a spherical symmetric Minkowski space–time is developed. The "passive" point of view is adapted, i.e., the space–time coordinates are not affected by group transformations; only the fields change under the action of the symmetry group. A particular ansatz for the gauge fields is chosen and the components of the strength tensor are computed. An analytical solution of Schwarzschild–deSitter type is obtained in the case of null torsion. It is concluded that the deSitter group can be considered as a "passive" gauge symmetry for gravitation. Because of their complexity, all the calculations, inclusive of the integration of the field equations, are performed using an analytical program conceived in GRTensorII for MapleV. The program allows one to compute (without using a metric) the strength tensor [Formula: see text], Riemann tensor [Formula: see text], Ricci tensor [Formula: see text], curvature scalar [Formula: see text], field equations, and the integration of these equations.

scholarly journals Nature itself in a mirror space–time

2015 ◽  
Vol 93 (10) ◽  
pp. 1005-1008 ◽  
Author(s):  
Rasulkhozha S. Sharafiddinov
Keyword(s):  
Dirac Equation ◽  
Minkowski Space ◽  
Space Time ◽  
Point Of View ◽  
Classical Solutions ◽  
Left Handed ◽  
Minkowski Space Time ◽  
Energy And Momentum ◽  
The Right ◽  
Structure Of Matter

The unity of the structure of matter fields with flavor symmetry laws involves that the left-handed neutrino in the field of emission can be converted into a right-handed one and vice versa. These transitions together with classical solutions of the Dirac equation testify in favor of the unidenticality of masses, energies, and momenta of neutrinos of the different components. If we recognize such a difference in masses, energies, and momenta, accepting its ideas about that the left-handed neutrino and the right-handed antineutrino refer to long-lived leptons, and the right-handed neutrino and the left-handed antineutrino are short-lived fermions, we would follow the mathematical logic of the Dirac equation in the presence of the flavor symmetrical mass, energy, and momentum matrices. From their point of view, nature itself separates Minkowski space into left and right spaces concerning a certain middle dynamical line. Thereby, it characterizes any Dirac particle both by left and by right space–time coordinates. It is not excluded therefore that whatever the main purposes each of earlier experiments about sterile neutrinos, namely, about right-handed short-lived neutrinos may serve as the source of facts confirming the existence of a mirror Minkowski space–time.

Relativistic synchronization of onboard clocks of navigation space vehicles with the aid of intersatellite measurements

2021 ◽  
pp. 56-66
Author(s):  
Nikolay N. Vasilyuk ◽  
Alexander P. Chervonkin
Keyword(s):  
Proper Time ◽  
Space Vehicle ◽  
Relativistic Correction ◽  
Point Of View ◽  
Space Vehicles ◽  
Satellite Measurements ◽  
Clock Drift ◽  
Coordinate Time ◽  
Upper Limit ◽  
Unambiguous Interpretation

The problem of the synchronization of onboard clocks of navigation satellites has considered from a relativistic point of view using the concept of “coordinate simultaneity”. This concept allows an unambiguous interpretation of the synchronization results within the framework of general relativity. The algorithm of intersatellite measurements processing has formulated in terms of a proper time of a space vehicle and the coordinate time of a reference frame. Rules of transformation between coordinate and proper time scales have indicated. An analytical expression has obtained for the periodic relativistic correction to the estimated value of the relative clock drift. This correction has expressed in terms of the coordinate time of a ground observer. The value of this correction exceeds the acceptable synchronization error and should be taken into account for the inter-satellite measurements processing. The error of the relativistic correction determination has calculated. This error provides an upper limit for the period of uploading of ephemeris data on the board of the space vehicle.

On the effects of the Lorentz symmetry violation in a magnetic medium at a low energy scenario

2018 ◽  
Vol 33 (36) ◽  
pp. 1850216
Author(s):  
K. Bakke ◽  
C. Salvador ◽  
H. Belich
Keyword(s):  
Magnetic Field ◽  
Scalar Field ◽  
Electric Field ◽  
Anharmonic Oscillator ◽  
Lorentz Symmetry ◽  
Low Energy ◽  
Symmetry Violation ◽  
Magnetic Medium ◽  
Energy Scenario ◽  
The Magnetic Field

It is analyzed the influence of a fixed background that breaks the Lorentz symmetry on the scalar field in the nonrelativistic regime. It is considered a medium with a nonuniform magnetization and the presence of an induced electric field. Then, due to the effects of the Lorentz symmetry violation, it is shown that the interaction of the scalar field with the magnetic field (produced by the nonuniform magnetization) and the induced electric field yields an effective potential analogous to the double anharmonic oscillator. Thereby, a discrete spectrum of energy can stem from the effects of the violation of the Lorentz symmetry on the scalar field.

scholarly journals K-essence model from the mechanical approach point of view: coupled scalar field and the late cosmic acceleration

2016 ◽  
Vol 2016 (07) ◽  
pp. 050-050 ◽  
Author(s):  
Mariam Bouhmadi-López ◽  
K. Sravan Kumar ◽  
João Marto ◽  
João Morais ◽  
Alexander Zhuk
Keyword(s):  
Scalar Field ◽  
Point Of View ◽  
Cosmic Acceleration ◽  
Mechanical Approach

Phenomenological approach to the viable nonmetric relativistic scalar 4-vector theory of gravitation

1995 ◽  
Vol 73 (3-4) ◽  
pp. 187-192 ◽  
Author(s):  
Alexander A. Vlasov
Keyword(s):  
Vector Field ◽  
Scalar Field ◽  
Gravitational Radiation ◽  
Phenomenological Approach ◽  
Gravitational Theory ◽  
Nonlinear Scalar Field ◽  
Minkowski Space Time ◽  
Vector Theory ◽  
Theory Of Gravitation ◽  
Relativistic Gravitational Theory

Contrary to the hypothesis that every viable theory of gravitation must be the metric one, this paper presents the example of nonmetric relativistic gravitational theory on the basis of Minkowski space-time, where the gravitation is described by a mixture of the nonlinear scalar field and the linear 4-vector field, compatible with all the known post-Newtonian gravitational tests, with tests on gravitational radiation from binary pulsar PSR 1913 + 16 and with the ordinary cosmological notions.

scholarly journals The shape dynamics description of gravity

2015 ◽  
Vol 93 (9) ◽  
pp. 956-962 ◽  
Author(s):  
Tim Koslowski
Keyword(s):  
Minkowski Space ◽  
Space Time ◽  
Point Of View ◽  
Small Scale ◽  
Shape Dynamics ◽  
Quantum Particles ◽  
Minkowski Space Time ◽  
Time Structures ◽  
Geometric Picture

Classical gravity can be described as a relational dynamical system without ever appealing to space–time or its geometry. This description is the so-called shape dynamics description of gravity. The existence of relational first principles from which the shape dynamics description of gravity can be derived is a motivation to consider shape dynamics (rather than general relativity) as the fundamental description of gravity. Adopting this point of view leads to the question: What is the role of space–time in the shape dynamics description of gravity? This question contains many aspects: Compatibility of shape dynamics with the description of gravity in terms of space–time geometry, the role of local Minkowski space, universality of space–time geometry and the nature of quantum particles, which can no longer be assumed to be irreducible representations of the Poincaré group. In this contribution I derive effective space–time structures by considering how matter fluctuations evolve along with shape dynamics. This evolution reveals an “experienced space–time geometry.” This leads (in an idealized approximation) to local Minkowski space and causal relations. The small-scale structure of the emergent geometric picture depends on the specific probes used to experience space–time, which limits the applicability of effective space–time to describe shape dynamics. I conclude with discussing the nature of quantum fluctuations (particles) in shape dynamics and how local Minkowski space–time emerges from the evolution of quantum particles.

scholarly journals The photino sector and a confining potential in a supersymmetric Lorentz-symmetry-violating model

2013 ◽  
Vol 73 (11) ◽  
Author(s):  
H. Belich ◽  
L. D. Bernald ◽  
Patricio Gaete ◽  
J. A. Helayël-Neto
Keyword(s):  
Lorentz Symmetry ◽  
Confining Potential

scholarly journals A NOTE ON SCALAR FIELD THEORY IN AdS3/CFT2

2010 ◽  
Vol 25 (14) ◽  
pp. 2815-2836
Author(s):  
PABLO MINCES
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Central Charge ◽  
Virasoro Algebra ◽  
Radial Coordinate ◽  
Poisson Brackets ◽  
Scalar Field Theory ◽  
Classical Level ◽  
Conjugate Momentum ◽  
Conformal Fields

We consider a scalar field theory in AdS d+1, and introduce a formalism on surfaces at equal values of the radial coordinate. In particular, we define the corresponding conjugate momentum. We compute the Noether currents for isometries in the bulk, and perform the asymptotic limit on the corresponding charges. We then introduce Poisson brackets at the border, and show that the asymptotic values of the bulk scalar field and the conjugate momentum transform as conformal fields of scaling dimensions Δ- and Δ+, respectively, where Δ± are the standard parameters giving the asymptotic behavior of the scalar field in AdS. Then we consider the case d = 2, where we obtain two copies of the Virasoro algebra, with vanishing central charge at the classical level. An AdS3/CFT2 prescription, giving the commutators of the boundary CFT in terms of the Poisson brackets at the border, arises in a natural way. We find that the boundary CFT is similar to a generalized ghost system. We introduce two different ground states, and then compute the normal ordering constants and quantum central charges, which depend on the mass of the scalar field and the AdS radius. We discuss certain implications of the results.

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