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 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.

scholarly journals From Fock’s transformation to de Sitter space

2015 ◽  
Vol 93 (7) ◽  
pp. 734-737 ◽  
Author(s):  
T. Foughali ◽  
A. Bouda
Keyword(s):  
Coordinate Transformation ◽  
Gordon Equation ◽  
De Sitter Space ◽  
Space Time ◽  
Poisson Brackets ◽  
De Sitter ◽  
Deformed Algebra ◽  
Klein Gordon ◽  
The Universe ◽  
Klein Gordon Equation

As with Deformed Special Relativity, we showed recently that the Fock coordinate transformation can be derived from a new deformed Poisson brackets. This approach allowed us to establish the corresponding momentum transformation that keeps invariant the four-dimensional contraction pμxμ. From the resulting deformed algebra, we construct the corresponding first Casimir. After first quantization, we show by using the Klein–Gordon equation that the space-time of the Fock transformation is the de Sitter one. As we will see, the invariant length representing the universe radius in the space-time of Fock’s transformation is exactly the radius of the embedded hypersurface representing the de Sitter space-time.

scholarly journals Notes on Conservation Laws, Equations of Motion of Matter, and Particle Fields in Lorentzian and Teleparallel de Sitter Space-Time Structures

2016 ◽  
Vol 2016 ◽  
pp. 1-27 ◽  
Author(s):  
Waldyr A. Rodrigues ◽  
Samuel A. Wainer
Keyword(s):  
Equations Of Motion ◽  
Killing Vector ◽  
De Sitter Space ◽  
Momentum Conservation ◽  
Space Time ◽  
Relativity Theory ◽  
De Sitter ◽  
Metric Tensor ◽  
Clifford Bundle ◽  
Time Structures

We discuss the physics of interacting fields and particles living in a de Sitter Lorentzian manifold (dSLM), a submanifold of a 5-dimensional pseudo-Euclidean (5dPE) equipped with a metric tensor inherited from the metric of the 5dPE space. The dSLM is naturally oriented and time oriented and is the arena used to study the energy-momentum conservation law and equations of motion for physical systems living there. Two distinct de Sitter space-time structuresMdSLandMdSTPare introduced given dSLM, the first equipped with the Levi-Civita connection of its metric field and the second with a metric compatible parallel connection. Both connections are used only as mathematical devices. Thus, for example,MdSLis not supposed to be the model of any gravitational field in the General Relativity Theory (GRT). Misconceptions appearing in the literature concerning the motion of free particles in dSLM are clarified. Komar currents are introduced within Clifford bundle formalism permitting the presentation of Einstein equation as a Maxwell like equation and proving that in GRT there are infinitely many conserved currents. We prove that in GRT even when the appropriate Killing vector fields exist it is not possible to define a conserved energy-momentum covector as in special relativistic theories.

scholarly journals EXPLICIT DERIVATION OF THE FLUCTUATION-DISSIPATION RELATION OF THE VACUUM NOISE IN THE N-DIMENSIONAL DE SITTER SPACE–TIME

2001 ◽  
Vol 16 (16) ◽  
pp. 2841-2857 ◽  
Author(s):  
T. MURATA ◽  
K. TSUNODA ◽  
K. YAMAMOTO
Keyword(s):  
Equations Of Motion ◽  
De Sitter Space ◽  
Space Time ◽  
Dirac Field ◽  
De Sitter ◽  
Fluctuation Dissipation ◽  
Dissipative Coefficient ◽  
Retarded Green Function ◽  
Kms Condition ◽  
Explicit Derivation

Motivated by a recent work by Terashima (Phys. Rev.D60, 084001), we revisit the fluctuation-dissipation (FD) relation between the dissipative coefficient of a detector and the vacuum noise of fields in curved space–time. In an explicit manner we show that the dissipative coefficient obtained from classical equations of motion of the detector and the scalar (or Dirac) field satisfies the FD relation associated with the vacuum noise of the field, which demonstrates that Terashima's prescription works properly in the N-dimensional de Sitter space–time. This practice is useful not only to reconfirm the validity of the use of the retarded Green function to evaluate the dissipative coefficient from the classical equations of motion but also to understand why the derivation works properly, which is discussed in connection with previous investigations on the basis of the Kubo–Martin–Schwinger (KMS) condition. Possible application to black hole space–time is also briefly discussed.

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.

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.

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