Nematic Structure of Space-Time and Its Topological Defects in 5D Kaluza-Klein Theory

AbstractIn this paper, we solve generalized KG-oscillator interacts with a uniform magnetic field in five-dimensional space-time background produced by topological defects under a linear confining potential using the Kaluza–Klein theory. We solve this equation and analyze an analogue of the Aharonov–Bohm effect for bound states. We observe that the energy level for each radial mode depend on the global parameters characterizing the space-time, the confining potential, and the magnetic field which shows a quantum effect.

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SPIN GAUGE THEORY OF GRAVITY IN CLIFFORD SPACE: A REALIZATION OF KALUZA–KLEIN THEORY IN FOUR-DIMENSIONAL SPACE–TIME

International Journal of Modern Physics A ◽

10.1142/s0217751x06031661 ◽

2006 ◽

Vol 21 (28n29) ◽

pp. 5905-5956 ◽

Cited By ~ 28

Author(s):

MATEJ PAVŠIČ

Keyword(s):

Dimensional Space ◽

Space Time ◽

Dirac Field ◽

Spin Connection ◽

Yang Mills ◽

Object A ◽

Klein Theory ◽

Dimensional Space Time ◽

The Right ◽

Kaluza Klein

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.

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FIVE-DIMENSIONAL KALUZA–KLEIN THEORY WITH A SOURCE

International Journal of Modern Physics A ◽

10.1142/s0217751x04019640 ◽

2004 ◽

Vol 19 (29) ◽

pp. 5043-5050 ◽

Cited By ~ 4

Author(s):

YONGGE MA ◽

JUN WU

Keyword(s):

Electromagnetic Field ◽

Test Particle ◽

Dimensional Reduction ◽

Dimensional Space ◽

Space Time ◽

Fifth Dimension ◽

Klein Theory ◽

Dimensional Space Time ◽

Kaluza Klein

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.

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A NEW APPROACH FOR SPACE-TIME-MATTER THEORY

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887813500047 ◽

2013 ◽

Vol 10 (04) ◽

pp. 1350004 ◽

Cited By ~ 1

Author(s):

AUREL BEJANCU

Keyword(s):

Tensor Field ◽

Differential Operators ◽

Space Time ◽

Horizontal Gradient ◽

Tensor Fields ◽

Tensor Calculus ◽

New Approach ◽

Horizontal Connection ◽

Klein Theory ◽

Kaluza Klein

This is the first paper in a series of three papers on a new approach for space-time-matter (STM) theory. The main purpose of this approach is to replace the Levi-Civita connection on the space-time from the classical Kaluza–Klein theory by what we call the Riemannian horizontal connection on the general Kaluza–Klein space. This is done by a development of a 4D tensor calculus whose geometrical objects live in a 5D space. The 4D tensor calculus and the Riemannian horizontal connection enable us to define in a 5D space some 4D differential operators: horizontal differential, horizontal gradient, horizontal divergence and horizontal Laplacian, which have a great role in the presentation of the STM theory in a covariant form. Finally, we introduce and study the horizontal electromagnetic tensor field, the horizontal Ricci tensor and the horizontal Einstein gravitational tensor field, which replace the well-known tensor fields from the classical Kaluza–Klein theory.

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Effects of Kaluza-Klein Theory and Potential on a Generalized Klein-Gordon Oscillator in the Cosmic String Space-Time

Advances in High Energy Physics ◽

10.1155/2020/8107025 ◽

2020 ◽

Vol 2020 ◽

pp. 1-15

Author(s):

Faizuddin Ahmed

Keyword(s):

Cosmic String ◽

Bound States ◽

Scalar Potential ◽

Space Time ◽

Relativistic Energy ◽

Klein Theory ◽

Klein Gordon ◽

Coulomb Type ◽

Relativistic Analogue ◽

Kaluza Klein

In this paper, we solve a generalized Klein-Gordon oscillator in the cosmic string space-time with a scalar potential of Cornell-type within the Kaluza-Klein theory and obtain the relativistic energy eigenvalues and eigenfunctions. We extend this analysis by replacing the Cornell-type with Coulomb-type potential in the magnetic cosmic string space-time and analyze a relativistic analogue of the Aharonov-Bohm effect for bound states.

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Unification of the Maxwell-Einstein-Dirac Correspondence

10.31237/osf.io/w8v4a ◽

2019 ◽

Author(s):

Wim Vegt

Keyword(s):

Field Theory ◽

General Relativity ◽

String Theory ◽

Dimensional Space ◽

Space Time ◽

Unified Field ◽

S Matrix ◽

Klein Theory ◽

Dimensional Space Time ◽

Kaluza Klein

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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SEMICLASSICAL DECAY OF KALUZA-KLEIN VACUUM IN HIGHER DERIVATIVE GRAVITY

Modern Physics Letters A ◽

10.1142/s0217732393001367 ◽

1993 ◽

Vol 08 (17) ◽

pp. 1621-1626

Author(s):

BIPLAB BHAWAL ◽

H.S. MANI

Keyword(s):

Physical Properties ◽

Ground State ◽

Space Time ◽

Higher Derivative ◽

Klein Theory ◽

Decay State ◽

Kaluza Klein

Semiclassical decay of the ground state of Kaluza-Klein theory has been studied in the context of higher derivative corrections to the Einstein action. Two solutions describing the decay state of the vacuum have been obtained. The first solution is asymptotic to the Witten bubble space-time, whereas the second solution is entirely new, but with the same physical properties. Properties of these solutions are discussed.

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Constraints on Space-Time-Matter Theory in the Framework of the Standard-Model Extension

Galaxies ◽

10.3390/galaxies9020026 ◽

2021 ◽

Vol 9 (2) ◽

pp. 26

Author(s):

James Overduin ◽

Hamna Ali ◽

Francis Walz

Keyword(s):

Standard Model ◽

Rest Mass ◽

Lorentz Violation ◽

Space Time ◽

Standard Model Extension ◽

Matter Theory ◽

Model Extension ◽

The Standard Model ◽

Klein Theory ◽

Kaluza Klein

We use experimental limits on Lorentz violation within the framework of the Standard-Model Extension to derive quantitative constraints on Space-Time-Matter theory, a version of Kaluza–Klein theory in which the cylinder condition is relaxed so that four-dimensional physics can in principle depend on the extra coordinates. The extra dimensions are not necessarily compact or length-like. We find that the associated variation in fundamental quantities such as rest mass must occur slowly, on cosmological scales.

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SPONTANEOUS CP VIOLATION FROM A QUATERNIONIC KALUZA–KLEIN THEORY

International Journal of Modern Physics A ◽

10.1142/s0217751x93001314 ◽

1993 ◽

Vol 08 (19) ◽

pp. 3263-3283 ◽

Cited By ~ 1

Author(s):

B. E. HANLON ◽

G. C. JOSHI

Keyword(s):

Cp Violation ◽

Universal Covering ◽

Special Linear Group ◽

Space Time ◽

Covariant Theory ◽

Universal Covering Group ◽

Covering Group ◽

Dimensional Minkowski Space ◽

Klein Theory ◽

Kaluza Klein

Motivated by the isomorphism between the universal covering group of the six-dimensional Lorentz group and the special linear group over the quaternions, a locally quaternionic covariant theory is postulated to exist in six space–time dimensions. Compactifying onto the space–time M4 ⊗ S2 a complex theory is retrieved on the four-dimensional Minkowski space with the essential quaternionic nature confined to S2. Quaternionic spinors are introduced and a dimensionally reduced theory recovered which exhibits a CP-violating effect via spontaneous symmetry breaking.

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THE EFFECTIVE ENERGY-MOMENTUM TENSOR IN KALUZA–KLEIN GRAVITY WITH LARGE EXTRA DIMENSIONS AND OFF-DIAGONAL METRICS

International Journal of Modern Physics D ◽

10.1142/s0218271802002682 ◽

2002 ◽

Vol 11 (09) ◽

pp. 1355-1380 ◽

Cited By ~ 26

Author(s):

J. PONCE DE LEON

Keyword(s):

Energy Momentum Tensor ◽

Dimensional Space ◽

Large Extra Dimensions ◽

Momentum Tensor ◽

Space Time ◽

Brane World ◽

Splitting Technique ◽

Klein Theory ◽

Electromagnetic Tensor ◽

Kaluza Klein

We consider a version of Kaluza–Klein theory where the cylinder condition is not imposed. The metric is allowed to have explicit dependence on the "extra" coordinate(s). This is the usual scenario in brane-world and space-time-matter theories. We extend the usual discussion by considering five-dimensional metrics with off-diagonal terms. We replace the condition of cylindricity by the requirement that physics in four-dimensional space-time should remain invariant under changes of coordinates in the five-dimensional bulk. This invariance does not eliminate physical effects from the extra dimension but separates them from spurious geometrical ones. We use the appropriate splitting technique to construct the most general induced energy-momentum tensor, compatible with the required invariance. It generalizes all previous results in the literature. In addition, we find two four-vectors, [Formula: see text] and [Formula: see text], induced by off-diagonal metrics, that separately satisfy the usual equation of continuity in 4D. These vectors appear as source-terms in equations that closely resemble the ones of electromagnetism. These are Maxwell-like equations for an antisymmetric tensor [Formula: see text] that generalizes the usual electromagnetic one. This generalization is not an assumption, but follows naturally from the dimensional reduction. Thus, if[Formula: see text] could be identified with the electromagnetic tensor, then the theory would predict the existence of classical magnetic charge and current. The splitting formalism used allows us to construct 4D physical quantities from five-dimensional ones, in a way that is independent from how we choose our space-time coordinates from those of the bulk.

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