Dereli physics department, middle east technical university, ankara, turkey r. In kaluzaklein theory this group suggests that gauge symmetry is the symmetry of circular compact dimensions. Apr 06, 2018 lecture 11 kaluza klein theory arindam kumar chatterjee. A spin1,4 gauge theory model with kaluzaklein symmetry. 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. 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. The action and field equations are a fivedimensional version of. Kaluzaklein theory of five dimensional space explained youtube. The purpose of these lectures is to give an introduction to gauge theories and the standard 14. Therefore we end up with a 4d theory of a massless gauge particle f. 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. What is an intuitive explanation of kaluzaklein theory.
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 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. Finsler and kaluzaklein gauge theories springerlink. From kaluza klein to noncommutative gravity theories. To the true believer, this is a statement not only of possibility but of necessity. 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. Abstract the kaluzaklein idea of extra spacetime dimensions continues to per. The transformations between possible gauges, called gauge transformations, form a lie groupreferred to as the. The finsler theory lends itself to an interpretation of the mapping operators as being geometrically similar to yangmills potentials. Kaluza theory gives rise to bransdicke scalar field.
From kaluza klein to noncommutative gauge theories of gravity george zoupanos physics department, national technical university of athens, 15780 zografou, greece. The original kaluza klein theory formulated a 5dimensional unified theory after the gravitation theory of einstein. Kaluza theory kaluzas idea three important aspects of kaluza theory. The gauge field lagrangian gauge invariant lagrangians for spin0 and sping. 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. Scalar fields in the nonsymmetric kaluzaklein jordan. In physics, kaluzaklein theory kk theory is a classical unified field theory of gravitation and electromagnetism built around the idea of a fifth dimension. On the kaluzaklein geometrization of the electroweak. 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.
World heritage encyclopedia, the aggregation of the largest online encyclopedias available, and the. Turn on a background gauge field in the six compact dimensions and along the cartan subalgebra of um. Citeseerx document details isaac councill, lee giles, pradeep teregowda. In many current uni cation theories involving gravity, it is natural to add compacti ed extra dimensions.
The original kaluzaklein theory was one of the first attempts to create an unified field theory i. 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. Kaluzaklein theory from the viewpoint of gauge theory of. Besides the particle physics models discussed above, gravity theories as gauge. Notice that the gauge couplings of 4 and 5 dimensional actions coef. A kaluzaklein interpretation of an extended gauge theory. Gauge theories used to model the results of physical experiments engage in. Oct 10, 2012 this kaluza klein theory had many fascinating consequences.
This is a pedagogical introduction to original kaluzaklein theory. Note that in yangmills theory, scalar fields transform covariantly under the gauge group g. Kaluza klein theory can ascribe gauge symmetry to be the geometric property of an assumed internal space. In this context, one may be interested in the idea of a uni. The kaluzaklein theory is a shining example of einsteins unification program. For a torus background the theory describes the full tower of kaluza klein modes or, in the dual frame, of the winding modes. The next step would be to try and unify gravity with the two other known forces of nature, the weak and strong forces. Niemi and sergey slizovskiy, embedding weinbergsalam in kaluza klein, arxiv. 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.
A kaluza klein interpretation of an extended gauge theory c. Does kaluzaklein theory successfully unify gr and em. We probe that the resultant theory can be understood as a gauge theory of linearized gravity in. A comparison of kaluza klein and finslertype gauge theories is sketched. The kaluza klein idea takes this one step further, proposing that there are more than one time and three space dimensions and that the curvature of the higherdimensional spacetime in the low energy approximation is perceived in the effective ordinary four dimensions as a unified theory of gravity and gauge. We develop a linearized five dimensional kaluzaklein theory as a gauge theory. E on a spacetime e plus a new term which is of 2nd order. No additional assumption is required for this in kaluzaklein theory. Supergravity and kaluzaklein dimensional reductions. Gauge field of the kaluzaklein theory in the presence of branes. The only issue is explicitly states is that fermions have to be included by hand. We obtain the modified kaluza klein metric as an invariant line element of a bundle. Thirdly, an explicit gauge field expectation value in a topologically nontrivial configuration can overcome the difficulty endemic to pure.
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. Klein principle to higher principal bundles and higher gauge fields. U1 gauge field of the kaluzaklein theory in the presence of branes. The description of possibility of kaluza klein theory to be the right unifying theory is. Introduction it is known that linearized gravity can be considered to be a gauge theory 1. 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. Conditions for exact equivalence of kaluzaklein and yang. Matter spinorial fields are extended to 5 dimensions by. Tucker department of physics, university of lancaster, lancaster, uk received 27 october 1981 a unified description of gravitation and electromagnetism interacting with. Kaluza, klein and their story of a fifth dimension plus. Early history of gauge theories and kaluzaklein theories. Generel relativity explains gravity with pure geometry. Kaluzaklein theory project gutenberg selfpublishing.
D ii sergey slizovskiy, higgs effect in consistent kaluza klein models with. Kaluza klein theories add extra spacetime dimensions to unify gravity and electromagnetism t. 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. U1 weak hypercharge gauge fields are obtained from a kaluza klein scheme, while the tetradic projections of the extradimensional contortion fields. 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. In a gauge theory there is a group of transformations of the field.
Since we aim to make this an interactive course, the schedule above may naturally. 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. 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. The prototype model for su 2 u1 electroweak interactions.
Here we obtain in a very simple way a generalization of this topology, valid for any gauge fields, by employing the projection theorem of kaluza klein theories page 144 of bleecker 3. The primary assumption of the original kaluzaklein theory other than a. A very elementary overview of the original kaluzaklein theory is presented. 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.
Gauge theories as a geometrical issue of a kaluzaklein. Kaluzaklein theory institute for theoretical physics. The cosmological constant problem and kaluzaklein theory. 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. Kaluzaklein theory of five dimensional space explained. Kaluza klein theory 11, 10d superstrings 12 and 11d supergravity. Klein 1926 start with a theory of einstein gravity in 5d. In this brief article we cannot deal with gauge theories in an extensive manner. Nuclear physics b209 1982 217233 northholland publishing company a spinl,4 gauge theory model with kaluzaklein symmetry t.
Its reduced action includes a higher derivative action in gravitation as well as a term linear inr. Things that have charge under electromagnetism would just be things that are moving in this circular fifth dimension. In physics, a gauge theory is a type of field theory in which the lagrangian does not change is invariant under local transformations from certain lie groups the term gauge refers to any specific mathematical formalism to regulate redundant degrees of freedom in the lagrangian. An introduction to kaluza klein theory an outlook on the role of the tools introduced in this course in modern physics and geometry. List of papers this thesis is based on the following papers, which are referred to in the text by their roman numerals. We consider kaluza klein theory based on the fiber bundle. Furthermore, we show that, by using this strategy, one can derive an uni.
Kaluzaklein unification in the poincare gauge theory of. 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. Specifically, the idea was to consider a pure 5d gravitational theory and reduce it to four dimensions resulting to a u1 gauge theory. Matter spinorial fields are extended to 5 dimensions by the choice of a proper dependence on the extracoordinate and of a normalization factor. To make a connection with our fourdimensional universe we need dimensional. 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. David bleecker, gauge theory and variational principles, dover publications, 1981. 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. Pdf linearized five dimensional kaluzaklein theory as a gauge.
Pdf an introduction to the kaluzaklein formulation researchgate. Dec 03, 2016 kaluzaklein theory of five dimensional space explained. The radius of this extra dimension would be related to the electric charge of particles. The resulting theory and its particle content is discussed.
Pdf we develop a linearized fivedimensional kaluzaklein theory as a gauge theory. Lecture 11 kaluza klein theory arindam kumar chatterjee. 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. Kaluzaklein theory and extra dimensions oxford scholarship. We develop a linearized five dimensional kaluza klein theory as a gauge theory. 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. 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. 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. In this seminar the 5dimensional kaluza klein theory is described thoroughly and at the end the extension to higher dimensions is mentioned. In the particular case of five dimensions, we show that using the kaluza klein mechanism, the field.
Gauge theory of kaluzaklein and winding modes nasaads. It was published in 1921 by german mathematician and physicist theodor kaluza and extended in 1926 by oskar klein. No mechanism is speci ed why it does not depend on the extra dimensions. This assumption is due to kaluza, who needed to make a more straightforward connection of his theory to the gauge transformation. The wiki article on kaluza klein theory says that this logic flounders on a number of issues. Actually, kaluza klein theory really has two key elements.
The kaluza klein vector is a gauge field for the dualitycovariantized courant bracket algebra rather than a lie algebra. From kaluzaklein to noncommutative gravity theories. On zeeman topology in kaluzaklein and gauge theories 2008. A comparison of kaluzaklein and finslertype gauge theories is sketched. Nuclear physics b209 1982 217233 northholland publishing company a spinl,4 gauge theory model with kaluza klein symmetry t. We present a geometrical unification theory in a kaluza klein approach that achieve the geometrization of a generic gauge theory bosonic component. The geometrization of the electroweak model is achieved in a fivedimensional riemanncartan framework. Doria university of warwick, mathematics lnstitute, cv7 4a2, coventry, england and r. Klein principle to higher principal bundles and higher gauge. We present a geometrical unification theory in a kaluzaklein approach that achieve the geometrization of a generic gauge theory bosonic component.
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