The kaluza klein vector is a gauge field for the dualitycovariantized courant bracket algebra rather than a lie algebra. We present a geometrical unification theory in a kaluzaklein approach that achieve the geometrization of a generic gauge theory bosonic component. Nuclear physics b209 1982 217233 northholland publishing company a spinl,4 gauge theory model with kaluza klein symmetry t. Abstract the kaluzaklein idea of extra spacetime dimensions continues to per. The other gauge theories emerged in a slow and complicated process gradually from gr, and their common geometrical structure best expressed in terms of connections of. We develop a linearized five dimensional kaluza klein theory as a gauge theory.
Klein principle to higher principal bundles and higher gauge fields. Conditions for exact equivalence of kaluzaklein and yang. The cosmological constant problem and kaluzaklein theory. In physics, kaluzaklein theory kk theory is a classical unified field theory of gravitation and electromagnetism built around the idea of a fifth dimension. Niemi and sergey slizovskiy, embedding weinbergsalam in kaluza klein, arxiv. Kaluzaklein unification in the poincare gauge theory of. U1 weak hypercharge gauge fields are obtained from a kaluza klein scheme, while the tetradic projections of the extradimensional contortion fields. Iv the early work of kaluza and klein 24 v klein s 1938 theory 32 vi the pauli letters to pais 35 vii yangmills theory 37.
This assumption is due to kaluza, who needed to make a more straightforward connection of his theory to the gauge transformation. Kaluza, klein and their story of a fifth dimension plus. Klein theory states that a metric on the total space of a principal bundle, if it is invariant under the principal action of p, naturally reduces to a metric together with a gauge field on the base manifold m. A very elementary overview of the original kaluzaklein theory is presented. E on a spacetime e plus a new term which is of 2nd order. Kaluza klein theory can ascribe gauge symmetry to be the geometric property of an assumed internal space. Thirdly, an explicit gauge field expectation value in a topologically nontrivial configuration can overcome the difficulty endemic to pure. In the particular case of five dimensions, we show that using the kaluza klein mechanism, the field. The words gauge eich transformation and gauge invariance appear for the rst time in this paper, but in the everyday meaning of change of length or change of calibration1. Citeseerx document details isaac councill, lee giles, pradeep teregowda. Apr 06, 2018 lecture 11 kaluza klein theory arindam kumar chatterjee. The wiki article on kaluza klein theory says that this logic flounders on a number of issues. The action and field equations are a fivedimensional version of. Kaluza klein reduction on s 1 and t n endimensional t string theory and endimensional elev m theory are at t presen our b est candidates for viding pro a uni ed description of all the tal fundamen forces in nature.
The radius of this extra dimension would be related to the electric charge of particles. D ii sergey slizovskiy, higgs effect in consistent kaluza klein models with. We obtain the modified kaluza klein metric as an invariant line element of a bundle. The transformations between possible gauges, called gauge transformations, form a lie groupreferred to as the. The next step would be to try and unify gravity with the two other known forces of nature, the weak and strong forces. Kaluzaklein theory from the viewpoint of gauge theory of. Pdf an introduction to the kaluzaklein formulation researchgate. The primary assumption of the original kaluzaklein theory other than a. This is the sense in which a gauge theory extends a global symmetry to a local symmetry, and closely resembles the historical development of the gauge theory of gravity known as general relativity. Kaluza theory kaluzas idea three important aspects of kaluza theory. Scalar fields in the nonsymmetric kaluzaklein jordan.
A comparison of kaluzaklein and finslertype gauge theories is sketched. The prototype model for su 2 u1 electroweak interactions. What is an intuitive explanation of kaluzaklein theory. On the kaluzaklein geometrization of the electroweak.
Yangmills lagrangian with the gauge group gfrom the nonsymmetric kaluza klein theory, plus a polynomial of 4th order with respect to the elds, plus a term which is quadratic with respect to the gauge derivative of the gauge derivative with respect to the connection e. We develop a linearized five dimensional kaluzaklein theory as a gauge theory. The purpose of these lectures is to give an introduction to gauge theories and the standard 14. Kaluzaklein theory is developed starting from the simplest example in which a single extra spatial dimension is compactified to a circle, and a single abelian gauge field emerges in four dimensions from the higherdimensional metric. Gauge theories used to model the results of physical experiments engage in. We show how it is possible to derive the gauge charge conservation from the invariance of the model under extradimensional translations and to geometrize gauge connections for spinors, thus we can. In kaluzaklein theory this group suggests that gauge symmetry is the symmetry of circular compact dimensions. The kaluza klein approach t of fusing gravity with gauge theory in a high dimensional spacetime is one of the most attractive ways of unifying the fundamental interactions in nature. The finsler theory lends itself to an interpretation of the mapping operators as being geometrically similar to yangmills potentials. Finsler and kaluzaklein gauge theories springerlink. The original kaluzaklein theory was one of the first attempts to create an unified field theory i. Kaluza theory gives rise to bransdicke scalar field.
David bleecker, gauge theory and variational principles, dover publications, 1981. In what follows, we will extend previous work 67 to show that the sign of depends on the signature of the 5d metric, and that its size depends on parameters in the metric. Kaluza klein theory is developed starting from the simplest example in which a single extra spatial dimension is compactified to a circle, and a single abelian gauge field emerges in four dimensions from the higherdimensional metric. We consider kaluza klein theory based on the fiber bundle. The geometrization of the electroweak model is achieved in a fivedimensional riemanncartan framework. Gauge field of the kaluzaklein theory in the presence of branes. Pdf we develop a linearized fivedimensional kaluzaklein theory as a gauge theory. Klein principle to higher principal bundles and higher gauge. Generel relativity explains gravity with pure geometry.
No mechanism is speci ed why it does not depend on the extra dimensions. We show that we can unify the gravitational and internal gauge interactions in a high dimensional riemanncartan spacetime in the spirit of kaluzaklein, if we identify some of the connection coefficients as yangmills potentials and if the dynamics of the spacetime is governed by the poincare gauge theory of gravitation whose lagrangian contains curvature and torsion squared. We present a geometrical unification theory in a kaluza klein approach that achieve the geometrization of a generic gauge theory bosonic component. Kaluzaklein theory of five dimensional space explained youtube. We then continue with supergravity theory where we show that it is invariant under supersymmetry transformations, it contains both d 4, n 1 and d 11, n 1 supergravity theories. For a torus background the theory describes the full tower of kaluza klein modes or, in the dual frame, of the winding modes. In this seminar the 5dimensional kaluza klein theory is described thoroughly and at the end the extension to higher dimensions is mentioned. Kaluzaklein theory institute for theoretical physics. Supergravity and kaluzaklein dimensional reductions. The description of possibility of kaluza klein theory to be the right unifying theory is.
Furthermore, we show that, by using this strategy, one can derive an uni. A kaluzaklein interpretation of an extended gauge theory. Kaluzaklein theory of five dimensional space explained. In physics, kaluza klein theory kk theory is a classical unified field theory of gravitation and electromagnetism built around the idea of a fifth dimension beyond the usual four of space and time and considered an important precursor to string theory. Does kaluzaklein theory successfully unify gr and em. A kaluza klein interpretation of an extended gauge theory c. Specifically, the idea was to consider a pure 5d gravitational theory and reduce it to four dimensions resulting to a u1 gauge theory. Kaluza klein theories add extra spacetime dimensions to unify gravity and electromagnetism t. To make a connection with our fourdimensional universe we need dimensional. In this approach one always considers a high dimensional riemannian spacetime and assumes that all but four of the dimensions are curled up, as a priori, to form. From kaluza klein to noncommutative gauge theories of gravity george zoupanos physics department, national technical university of athens, 15780 zografou, greece.
Kaluzaklein theory and extra dimensions oxford scholarship. This is a pedagogical introduction to original kaluzaklein theory. A textbook account of the geometry behind the lorentz force in the kaluza klein mechanism the idea that geodesics on the gauge bundle project to curved trajectories on the base manifold can be found in the introduction of chapter 1 and in chapters 9 and 10 of. Matter spinorial fields are extended to 5 dimensions by the choice of a proper dependence on the extracoordinate and of a normalization factor. Note that in yangmills theory, scalar fields transform covariantly under the gauge group g. We probe that the resultant theory can be understood as a gauge theory of linearized gravity in. Dec 03, 2016 kaluzaklein theory of five dimensional space explained. Gauge theory of kaluzaklein and winding modes nasaads.
On zeeman topology in kaluzaklein and gauge theories 2008. World heritage encyclopedia, the aggregation of the largest online encyclopedias available, and the. Introduction it is known that linearized gravity can be considered to be a gauge theory 1. Its reduced action includes a higher derivative action in gravitation as well as a term linear inr. In modern geometry, the extra fifth dimension can be understood to be the circle group u1, as electromagnetism can essentially be formulated as a gauge theory on a fiber bundle, the circle bundle, with gauge group u1. Actually, kaluza klein theory really has two key elements. Lecture 11 kaluza klein theory arindam kumar chatterjee. From kaluzaklein to noncommutative gravity theories. Tucker department of physics, university of lancaster, lancaster, uk received 27 october 1981 a unified description of gravitation and electromagnetism interacting with. Therefore we end up with a 4d theory of a massless gauge particle f. The gauge field lagrangian gauge invariant lagrangians for spin0 and sping. Besides the particle physics models discussed above, gravity theories as gauge. In this brief article we cannot deal with gauge theories in an extensive manner.
Klein 1926 start with a theory of einstein gravity in 5d. It is shown that the two can be related by a mapping between fiber spaces which is equivalent to a transformation from one representation of the gauge group to another. Notice that the gauge couplings of 4 and 5 dimensional actions coef. An introduction to kaluza klein theory an outlook on the role of the tools introduced in this course in modern physics and geometry. Kaluzaklein theory project gutenberg selfpublishing. A comparison of kaluza klein and finslertype gauge theories is sketched.
Doria university of warwick, mathematics lnstitute, cv7 4a2, coventry, england and r. In many current uni cation theories involving gravity, it is natural to add compacti ed extra dimensions. It not only unifies gravitation with electromagnetism in a gr theory with a 5d spacetime but also suggests a possible interpretation of the charge space and gauge symmetry as reflecting the existence of a compactified extra dimension. U1 gauge field of the kaluzaklein theory in the presence of branes.
The resulting theory and its particle content is discussed. This approach relates zeeman topologies and kaluza klein, therefore gauge theories, what brings insights and points in the direction of a completely geometric. The kaluzaklein theory is a shining example of einsteins unification program. Kaluza klein theory 11, 10d superstrings 12 and 11d supergravity. The original kaluza klein theory formulated a 5dimensional unified theory after the gravitation theory of einstein. Dereli physics department, middle east technical university, ankara, turkey r. No additional assumption is required for this in kaluzaklein theory.
Gauge theory, class of quantum field theory, a mathematical theory involving both quantum mechanics and einsteins special theory of relativity that is commonly used to describe subatomic particles and their associated wave fields. In this context, one may be interested in the idea of a uni. To the true believer, this is a statement not only of possibility but of necessity. In a gauge theory there is a group of transformations of the field. The kaluzaklein mechanism, named after theodor kaluza and oskar klein, is the observation that pure gravity on a product spacetime with fixed metric on looks on, as an effective field theory, like gravity coupled to yangmills theory einsteinyangmills theory for gauge. From kaluza klein to noncommutative gravity theories. Oct 10, 2012 this kaluza klein theory had many fascinating consequences. It was published in 1921 by german mathematician and physicist theodor kaluza and extended in 1926 by oskar klein. The first attempt in the concept of the dimensional reduction of a higherdimensional theory, in which 4d theories are obtained starting from a unified theory, was that of kaluza klein,1. Pdf linearized five dimensional kaluzaklein theory as a gauge. Tucker department of physics, university of lancaster, lancaster, uk received 27 october 1981 a unified description of gravitation and electromagnetism interacting with dirac spinors is. Early history of gauge theories and kaluzaklein theories. Matter spinorial fields are extended to 5 dimensions by.
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