INDUCING CHARGES AND CURRENTS FROM EXTRA DIMENSIONS

2008 ◽  
Vol 23 (03) ◽  
pp. 197-203 ◽  
Author(s):  
M. A. S. CRUZ ◽  
F. DAHIA ◽  
C. ROMERO

In a particular variant of Kaluza–Klein theory, the so-called induced-matter theory (IMT), it is shown that any configuration of matter may be geometrically induced from a five-dimensional vacuum space. By using a similar approach we show that any distribution of charges and currents may also be induced from a five-dimensional space. Although in the case of IMT the geometry is Riemannian and the fundamental equations are the five-dimensional Einstein equations in vacuum, here we consider a Minkowskian geometry and five-dimensional Maxwell equations in vacuum.

2002 ◽  
Vol 17 (29) ◽  
pp. 4287-4295
Author(s):  
C. ROMERO

We briefly review the problem of embedding the spacetime in five dimensions and discuss the geometrical structure of a non-compactified version of Kaluza-Klein theory, known as induced-matter theory. We also highlight the importance of the embedding theorems of differential geometry in the context of embedding theories and present new results which may be considered as extensions of the Campbell-Magaard theorem.


2000 ◽  
Vol 09 (04) ◽  
pp. 445-458 ◽  
Author(s):  
W. N. SAJKO

We give a Hamiltonian treatment of 5D vacuum Kaluza–Klein theory that is unrestricted in the extra coordinate dependence. When the extra coordinate dependence is removed from the 5D metric we recover the Hamiltonian for gravity and electromagetism nonminimally coupled to a scalar field. The energies of 5D uncharged and charged soliton solutions are calculated via the Hamiltonian and are identified with the total mass. The expressions for the total mass are shown to agree with the sum of scalar and gravitational masses calculated from the scalar-tensor induced matter in 4D. A semi-classical derivation of the temperature for the uncharged solitons is calculated and it is shown that the only nontrivial member of the 5D class is the 4D Schwarzschild solution trivially embedded in 5D, and therefore the entropy obeys the one-quarter area law.


2006 ◽  
Vol 21 (28n29) ◽  
pp. 5905-5956 ◽  
Author(s):  
MATEJ PAVŠIČ

A theory in which four-dimensional space–time is generalized to a larger space, namely a 16-dimensional Clifford space (C-space) is investigated. Curved Clifford space can provide a realization of Kaluza–Klein. A covariant Dirac equation in curved C-space is explored. The generalized Dirac field is assumed to be a polyvector-valued object (a Clifford number) which can be written as a superposition of four independent spinors, each spanning a different left ideal of Clifford algebra. The general transformations of a polyvector can act from the left and/or from the right, and form a large gauge group which may contain the group U (1) × SU (2) × SU (3) of the standard model. The generalized spin connection in C-space has the properties of Yang–Mills gauge fields. It contains the ordinary spin connection related to gravity (with torsion), and extra parts describing additional interactions, including those described by the antisymmetric Kalb–Ramond fields.


1986 ◽  
Vol 169 (4) ◽  
pp. 327-332 ◽  
Author(s):  
M. Chaichian ◽  
A.P. Demichev ◽  
N.F. Nelipa

2004 ◽  
Vol 19 (29) ◽  
pp. 5043-5050 ◽  
Author(s):  
YONGGE MA ◽  
JUN WU

A free test particle in five-dimensional Kaluza–Klein space–time will show its electricity in the reduced four-dimensional space–time when it moves along the fifth dimension. In the light of this observation, we study the coupling of a five-dimensional dust field with the Kaluza–Klein gravity. It turns out that the dust field can curve the five-dimensional space–time in such a way that it provides exactly the source of the electromagnetic field in the four-dimensional space–time after the dimensional reduction.


2019 ◽  
Author(s):  
Wim Vegt

Albert Einstein, Lorentz and Minkowski published in 1905 the Theory of Special Relativity and Einstein published in 1915 his field theory of general relativity based on a curved 4-dimensional space-time continuum to integrate the gravitational field and the electromagnetic field in one unified field. Since then the method of Einstein’s unifying field theory has been developed by many others in more than 4 dimensions resulting finally in the well-known 10-dimensional and 11-dimensional “string theory”. String theory is an outgrowth of S-matrix theory, a research program begun by Werner Heisenberg in 1943 (following John Archibald Wheeler‘s(3) 1937 introduction of the S-matrix), picked up and advocated by many prominent theorists starting in the late 1950’s.Theodor Franz Eduard Kaluza (1885-1954), was a German mathematician and physicist well-known for the Kaluza–Klein theory involving field equations in curved five-dimensional space. His idea that fundamental forces can be unified by introducing additional dimensions re-emerged much later in the “String Theory”.The original Kaluza-Klein theory was one of the first attempts to create an unified field theory i.e. the theory, which would unify all the forces under one fundamental law. It was published in 1921 by Theodor Kaluza and extended in 1926 by Oskar Klein. The basic idea of this theory was to postulate one extra compactified space dimension and introduce nothing but pure gravity in a new (1 + 4)-dimensional space-time. Klein suggested that the fifth dimension would be rolled up into a tiny, compact loop on the order of 10-35 [m]The presented "New Unification Theory" unifies Classical Electrodynamics with General Relativity and Quantum Physics


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