Some properties of the p-brane model with the quadratic lagrangian

1999 ◽  
Vol 4 ◽  
pp. 97-112
Author(s):  
P. Miškinis
Keyword(s):  
Dimensional Space ◽  
Equations Of Motion ◽  
Critical Dimension ◽  
Space Time ◽  
Brane Model ◽  
Arbitrary Topology ◽  
General Properties ◽  
Dimensional Space Time ◽  
Dimensional Surface

Some general properties of the relativistic p-dimensional surface imbedded into D-dimensional space-time and its reduction to the simplest case of the quadratic Lagrangian are considered. The solutions of the equations of motion of such model for the p-brane with arbitrary topology and massless eigenstates, as well as with critical dimension after quantization are presented. Some generalizations for the supermembrane are discussed.

scholarly journals Dynamical Codimension – 2 Brane in a Warped Six Dimensional Space-time

2018 ◽  
Vol 28 (3) ◽  
pp. 277
Author(s):  
Phan Hong Lien
Keyword(s):  
Einstein Equation ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Space Time ◽  
Cosmological Evolution ◽  
System Of Equations ◽  
Dimensional Space Time ◽  
Six Dimensions ◽  
Bulk Space

In this paper we present the Einstein equation extended in six-dimensions (6D) from the formation of codimension-2 brane, which is created by a 4-brane and 4-anti brane moving in the warped 6D “bulk” space-time. The system of equations of motion for the dynamical codimension - 2 brane has been derived to describe the cosmological evolution on the probe branes. Some cosmological consequences are investigated.

Classical strings in ten dimensions

1987 ◽  
Vol 414 (1847) ◽  
pp. 423-431 ◽  
Keyword(s):  
General Solution ◽  
Linear Space ◽  
Significant Role ◽  
Algebraic Variety ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Space Time ◽  
Relativistic String ◽  
Dimensional Space Time ◽  
The Given

This article analyses the motion of a classical relativistic string in flat complex ten-dimensional space-time. A general solution is presented for the equations of motion. The solution is given in terms of essentially freely specifiable functions. In deriving these results extensive use is made of spinors for ten dimensions, the basic properties of which are described in some detail. In particular, a significant role is played by those spinors in ten dimensions that satisfy the ‘purity’ property of E. Cartan. These constitute an eleven-dimensional algebraic variety V in the sixteen-dimensional linear space of reduced (Weyl) spinors for the group SO(10). A general classical relativistic string in ten dimensions can be represented by means of a set of arbitrarily specifiable twice-differentiable curves in V . As a by-product of the investigation a general solution is also given for the equations of motion of a classical relativistic string in eight­-dimensional space-time. Seldom have thinkers become so absorbed in revery, or so far estranged from reality, as to imagine for our space a number of dimensions exceeding the three of the given space of sense ...(Ernst Mach, 1906)

scholarly journals THE PRINCIPLE OF LEAST ACTION FOR TEST PARTICLES IN A FOUR-DIMENSIONAL SPACE–TIME EMBEDDED IN 5D

2008 ◽  
Vol 23 (04) ◽  
pp. 249-259 ◽  
Author(s):  
J. PONCE DE LEON
Keyword(s):  
Dimensional Space ◽  
Equations Of Motion ◽  
Rest Mass ◽  
Geodesic Equation ◽  
Space Time ◽  
Geodesic Motion ◽  
Least Action ◽  
Test Particles ◽  
Principle Of Least Action ◽  
Dimensional Space Time

It is well known that, in the five-dimensional scenario of braneworld and space–time-mass theories, geodesic motion in 5D is observed to be non-geodesic in 4D. Usually, the discussion is purely geometric and based on the dimensional reduction of the geodesic equation in 5D, without any reference to the test particle whatsoever. In this work we obtain the equation of motion in 4D directly from the principle of least action. So our main thrust is not the geometry but the particle observed in 4D. A clear physical picture emerges from our work. Specifically, that the deviation from the geodesic motion in 4D is due to the variation of the rest mass of a particle, which is induced by the scalar field in the 5D metric and the explicit dependence of the space–time metric on the extra coordinate. Thus, the principle of least action not only leads to the correct equations of motion, but also provides a concrete physical meaning for a number of algebraic quantities appearing in the geometrical reduction of the geodesic equation.

Topology knots and hierarchy problem

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Quantum Theory ◽  
String Theory ◽  
Quantum Gravity ◽  
Dimensional Space ◽  
Space Time ◽  
Elementary Particles ◽  
Hierarchy Problem ◽  
Topological Quantum ◽  
Dimensional Space Time ◽  
New Formula

Many approaches to quantum gravity consider the revision of the space-time geometry and the structure of elementary particles. One of the main candidates is string theory. It is possible that this theory will be able to describe the problem of hierarchy, provided that there is an appropriate Calabi-Yau geometry. In this paper we will proceed from the traditional view on the structure of elementary particles in the usual four-dimensional space-time. The only condition is that quarks and leptons should have a common emerging structure. When a new formula for the mass of the hierarchy is obtained, this structure arises from topological quantum theory and a suitable choice of dimensional units.

Electromagnetic Casimir effect of concentric cylinders in (D + 1)-dimensional space–time

2019 ◽  
Vol 34 (08) ◽  
pp. 1950035
Author(s):  
Chun Yong Chew ◽  
Yong Kheng Goh
Keyword(s):  
Boundary Condition ◽  
Interaction Energy ◽  
Casimir Effect ◽  
Dimensional Space ◽  
Order Term ◽  
Perturbation Technique ◽  
Space Time ◽  
Concentric Cylinders ◽  
Dimensional Minkowski Space ◽  
Dimensional Space Time

We study the electromagnetic Casimir interaction energy between two parallel concentric cylinders in [Formula: see text]-dimensional Minkowski space–time for different combinations of perfectly conducting boundary condition and infinitely permeable boundary condition. We consider two cases where one cylinder is outside each other and where one is inside the other. By solving the equation of motion and computing the TGTG formulas, explicit formulas for the Casimir interaction energy can be derived and asymptotic behavior of the Casimir interaction energy in the nanoregime is calculated by using perturbation technique. We computed the interaction energy analytically up to next-to-leading order term.

scholarly journals TRAVERSABLE WORMHOLES IN A STRING CLOUD

2008 ◽  
Vol 17 (08) ◽  
pp. 1179-1196 ◽  
Author(s):  
MARTÍN G. RICHARTE ◽  
CLAUDIO SIMEONE
Keyword(s):  
Thin Shell ◽  
Dimensional Space ◽  
Space Time ◽  
Exotic Matter ◽  
Spherically Symmetric ◽  
Related Model ◽  
Traversable Wormholes ◽  
Dimensional Space Time ◽  
Thin Shell Wormholes ◽  
The Stability

We study spherically symmetric thin shell wormholes in a string cloud background in (3 + 1)-dimensional space–time. The amount of exotic matter required for the construction, the traversability and the stability of such wormholes under radial perturbations are analyzed as functions of the parameters of the model. In addition, in the appendices a nonperturbative approach to the dynamics and a possible extension of the analysis to a related model are briefly discussed.

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