On the dynamics of spinning particle in nonlinear relativity

2021 ◽  
Vol 36 (06) ◽  
pp. 2150048
Author(s):  
H. Guergouri ◽  
T. Foughali
Keyword(s):  
Minkowski Space ◽  
Equations Of Motion ◽  
Space Time ◽  
Conformally Flat ◽  
De Sitter ◽  
Spinning Particle ◽  
Spinning Particles ◽  
Minkowski Space Time ◽  
Conformally Flat Metric ◽  
Uniform Electromagnetic Field

In order to study the dynamics of spinning particles in R-Minkowski space–time, first we have used the Bhabha–Corben model to describe how a spinning particle behave in a uniform electromagnetic field. Then, to extend the Mathisson–Papapetrou equations to R-Minkowski space–time, that correspond to de Sitter space–time given by a conformally flat metric, it was necessary to determine the Killing vectors, which allowed us to find the equations of motion that describe the dynamics of spinning particles.

scholarly journals Elastic shocks in relativistic rigid rods and balls

2019 ◽  
Vol 475 (2225) ◽  
pp. 20180858 ◽  
Author(s):  
João L. Costa ◽  
José Natário
Keyword(s):  
Free Boundary ◽  
Minkowski Space ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Time Derivative ◽  
Space Time ◽  
Spherically Symmetric ◽  
Soft Phase ◽  
Minkowski Space Time ◽  
Dimensional Minkowski Space

We study the free boundary problem for the ‘hard phase’ material introduced by Christodoulou in (Christodoulou 1995 Arch. Ration. Mech. Anal. 130 , 343–400), both for rods in (1 + 1)-dimensional Minkowski space–time and for spherically symmetric balls in (3 + 1)-dimensional Minkowski space–time. Unlike Christodoulou, we do not consider a ‘soft phase’, and so we regard this material as an elastic medium, capable of both compression and stretching. We prove that shocks must be null hypersurfaces, and derive the conditions to be satisfied at a free boundary. We solve the equations of motion of the rods explicitly, and we prove existence of solutions to the equations of motion of the spherically symmetric balls for an arbitrarily long (but finite) time, given initial conditions sufficiently close to those for the relaxed ball at rest. In both cases we find that the solutions contain shocks if and only if the pressure or its time derivative do not vanish at the free boundary initially. These shocks interact with the free boundary, causing it to lose regularity.

scholarly journals NEGATIVE NORM STATES IN DE SITTER SPACE AND QFT WITHOUT RENORMALIZATION PROCEDURE

2002 ◽  
Vol 11 (06) ◽  
pp. 509-518 ◽  
Author(s):  
MOHAMMAD VAHID TAKOOK
Keyword(s):  
Minkowski Space ◽  
De Sitter Space ◽  
Infrared Divergence ◽  
Space Time ◽  
Ultraviolet Divergence ◽  
De Sitter ◽  
Physical Content ◽  
Negative Norm ◽  
Minkowski Space Time ◽  
Loop Approximation

In recent papers,1,2 it has been shown that the presence of negative norm states or negative frequency solutions are indispensable for a fully covariant quantization of the minimally coupled scalar field in de Sitter space. Their presence, while leaving unchanged the physical content of the theory, offers the advantage of eliminating any ultraviolet divergence in the vacuum energy2 and infrared divergence in the two point function.3 We attempt here to extend this method to the interacting quantum field in Minkowski space-time. As an illustration of the procedure, we consider the λϕ4 theory in Minkowski space-time. The mathematical consequences of this method is the disappearance of the ultraviolet divergence to the one-loop approximation. This means, the effect of these auxiliary negative norm states is to allow an automatic renormalization of the theory in this approximation.

A STRING MODEL FOR D-DIMENSIONAL DE SITTER SPACE–TIME AND EQUATIONS OF MOTION

2005 ◽  
Vol 20 (26) ◽  
pp. 6065-6081
Author(s):  
PAUL BRACKEN
Keyword(s):  
Evolution Equations ◽  
Gordon Equation ◽  
Equations Of Motion ◽  
String Model ◽  
De Sitter Space ◽  
Space Time ◽  
System Of Equations ◽  
De Sitter ◽  
Minkowski Space Time ◽  
Dimensional Minkowski Space

De Sitter space–time is considered to be represented by a D-dimensional hyperboloid embedded in (D+1)-dimensional Minkowski space–time. The string equation is derived from a string action which contains a Lagrange multiplier to restrict coordinates to de Sitter space–time. The string system of equations is equivalent to a type of generalized sinh–Gordon equation. The evolution equations for all the variables including the coordinates and their derivatives are obtained for D=2,3 and 4.

scholarly journals Particle creation with excited de Sitter modes

2015 ◽  
Vol 93 (12) ◽  
pp. 1466-1469 ◽  
Author(s):  
M. Mohsenzadeh ◽  
E. Yusofi ◽  
M.R. Tanhayi
Keyword(s):  
Power Spectrum ◽  
Minkowski Space ◽  
Particle Creation ◽  
Space Time ◽  
Time Limit ◽  
De Sitter ◽  
Past Time ◽  
Time Symmetry ◽  
Minkowski Space Time ◽  
Initial States

Recently, we introduced exited de Sitter modes to study the power spectrum that was finite in Krein space quantization and the trans-Plankian corrections because of the exited mode being nonlinear (M. Mohsenzadeh et al. Eur. Phys. J. C, 74, 2920 (2014) doi:10.1140/epjc/s10052-014-2920-5 ). It was shown that the de Sitter limit of corrections reduces to that obtained via several previous conventional methods; moreover, with such modes the space–time symmetry becomes manifest. In this paper, inspired by the Krein method and using exited de Sitter modes as the fundamental initial states during the inflation, we calculate particle creation in the spatially flat Robertson–Walker space–time. It is shown that in de Sitter and Minkowski space–time in the far past time limit, our results coincide with the standard results.

scholarly journals DIRAC FIELDS ON SPACELIKE HYPERSURFACES, THEIR REST-FRAME DESCRIPTION AND DIRAC OBSERVABLES

1999 ◽  
Vol 14 (12) ◽  
pp. 1877-1910 ◽  
Author(s):  
FRANCESCO BIGAZZI ◽  
LUCA LUSANNA
Keyword(s):  
Electromagnetic Field ◽  
Minkowski Space ◽  
Electric Current ◽  
Spin Structure ◽  
Rest Frame ◽  
Space Time ◽  
Spinning Particles ◽  
Dirac Fields ◽  
Minkowski Space Time ◽  
Spacelike Hypersurfaces

Grassmann-valued Dirac fields together with the electromagnetic field (the pseudo-classical basis of QED) are reformulated on spacelike hypersurfaces in Minkowski space–time and then restricted to Wigner hyperplanes to get their description in the rest-frame Wigner-covariant instant form of dynamics. The canonical reduction to the Wigner-covariant Coulomb gauge is done in the rest frame. It is shown, on the basis of a geometric inconsistency, that the description of fermions is incomplete, because there is no bosonic carrier of the spin structure describing the trajectory of the electric current in Minkowski space–time, as it was already emphasized in connection with the first quantization of spinning particles in a previous paper.

LIFETIME OF A DE SITTER PARTICLE

2008 ◽  
Vol 05 (08) ◽  
pp. 1243-1254
Author(s):  
HENRI EPSTEIN
Keyword(s):  
Perturbation Theory ◽  
Minkowski Space ◽  
Principal Series ◽  
De Sitter Space ◽  
Space Time ◽  
De Sitter ◽  
Complementary Series ◽  
First Order ◽  
Interaction Terms ◽  
Minkowski Space Time

The familiar rule which, in Minkowski space-time, forbids the decay of a particle into heavier products, does not hold in de Sitter space-time. We study, in first order of perturbation theory, the decay of a particle of the "principal series" and show that it may decay into two particles of any of the "principal" or "complementary" series (with suitable interaction terms). Spectral conditions reappear in the decay of a "complementary" particle: but its lifetime is 0.

On generalized partially null Mannheim curves in Minkowski space-time

2016 ◽  
Vol 46 (1) ◽  
pp. 159-170 ◽  
Author(s):  
Emilija Nešović ◽  
Milica Grbović
Keyword(s):  
Minkowski Space ◽  
Space Time ◽  
Minkowski Space Time

scholarly journals A MAXWELL-LIKE FORMULATION OF GRAVITATIONAL THEORY IN MINKOWSKI SPACE–TIME

2007 ◽  
Vol 16 (06) ◽  
pp. 1027-1041 ◽  
Author(s):  
EDUARDO A. NOTTE-CUELLO ◽  
WALDYR A. RODRIGUES
Keyword(s):  
Gravitational Field ◽  
Minkowski Space ◽  
Gravitational Theory ◽  
Space Time ◽  
Lorentzian Geometry ◽  
Field Equations ◽  
Yang Mills ◽  
Minkowski Space Time ◽  
Clifford Bundle ◽  
Gauge Fixing

Using the Clifford bundle formalism, a Lagrangian theory of the Yang–Mills type (with a gauge fixing term and an auto interacting term) for the gravitational field in Minkowski space–time is presented. It is shown how two simple hypotheses permit the interpretation of the formalism in terms of effective Lorentzian or teleparallel geometries. In the case of a Lorentzian geometry interpretation of the theory, the field equations are shown to be equivalent to Einstein's equations.

Sign in / Sign up

Export Citation Format

Share Document