Kaluza, klein and their story of a fifth dimension plus. In opposition to some dissenters, i show in greater detail how unification works in the practice of science and how it relates to explanation, simplicity, theory validation, etc. Early history of gauge theories and kaluzaklein theories. Distinguished bundle metrics are described and the computation of the corresponding higher dimensional einsteinhilbert actions and their dimensional reductions.
Regarding some questions on the talk page about the group theory sections, i cannot speak to that. We show that in spite of their seeming similarity they constitute rather distinct proposals as far as their geometrical structure is concerned. Let us assume that the invariance group g 5 of the admissible coordinate transformations is the direct product g 4 xg 1, where g 4 is the manifold general group of m 4 i. It was published in 1921 by german mathematician and physicist theodor kaluza and extended in 1926 by oskar klein. The nonsymmetric kaluzaklein theory and modern physics a. Kaluzaklein theory in quantum gravity abstract in this paper, we discuss a method which aims to combine kaluzaklein theory with causalset theory. Pdf an introduction to the kaluzaklein formulation researchgate. A very elementary overview of the original kaluza klein theory is presented, suitable for undergraduates who want to learn the basic mathematical formalism behind a revolutionary idea that was proposed one hundred years ago, yet today serves as the template for modern higherdimensional particle and gravity theories. First, we describe kaluzas original \cylinder condition and how this allows for the uni cation of einstein gravity and electromagnetism in a vedimensional framework. In physics, kaluzaklein theory kk theory is a classical unified field theory of gravitation and. A modern aspect that we do wish to mention, however, is the emergence of both gauge theory and dimensional reduction. The cosmological constant problem and kaluzaklein theory.
Kevin costello, notes on supersymmetric and holomorphic field theories in dimensions 2 and 4 arxiv. A formalization of kaluza klein compactification in perturbation theory formalized by factorization algebras with values in bvcomplexes is in section 19 of. Copyright q 1999 by world scientific publishing co. Oct 10, 2012 kaluza and klein showed, using general relativity, that this extra dimension would still have an effect on the space around us. Buy modern kaluzaklein theories frontiers in physics on free shipping on qualified orders. On the kaluza klein geometrization of the electroweak model within a gauge theory of the 5dimensional lorentz group lecian, orchidea maria et al. Kaluzaklein gravity in the context of modern embedding theories of spacetime article pdf available in gravitation and cosmology 10. We also discuss some cosmological implications of the noncompacti ed theory at the end of this paper. Modern kaluzaklein theories have three main features. Early history of gauge theories and kaluza klein theories, with a glance at recent developments lochlain oraifeartaigh dublin institute for advanced studies, dublin 4, ireland. In particular they showed that the effect of gravity in that very small fifth dimension would actually appear to us, from our largerscale perspective, as electromagnetism.
Causal anomalies in two kaluza klein gravity theories are examined, particularly as to whether these theories permit solutions in which the causality principle is violated. Various geometrical aspects of kaluza klein theories are studied for extended spacetime manifolds, having the structure of fibre bundles which are associated to principle fibre bundles and whose standard fibres are homogeneous spaces. Unification and explanation in early kaluzaklein theories. Apr 28, 20 this is where theories like string theory come in. No mechanism is speci ed why it does not depend on the extra dimensions. Although kaluza klein theory is generally considered unphysical, the founding principle may yet offer us a path to a unified theory of physics.
A modern kind of kaluzaklein theory is represented by the theory of a universal extra dimension ued, which can be seen as a generalization of the standard model of particle physics to. World heritage encyclopedia, the aggregation of the largest online encyclopedias available, and the. Wesson collates technical results on 5d relativity with the aim of showing how far einsteins vision of physics as geometry can be realized. Kaluza klein gravity in the context of modern embedding theories of spacetime article pdf available in gravitation and cosmology 10. 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. Kaluza theory kaluza s idea three important aspects of kaluza theory. Otherwise, i would take the later stuff in the article with a grain of salt. It is shown that the four dimensional theory, as we observe it today, can be obtained. Modern kaluza klein theories, by contrast, routinely require the addition of explicit higherdimensional matter fields in order to achieve successful compactification among other things. A brief summary of kaluzaklein theory jonah miller jonah.
In this seminar the 5dimensional kaluza klein theory is described thoroughly and at the end the extension to higher dimensions is mentioned. In particular, we look at the concept of coarsegraining and at two definitions of the ricci scalar in a causalset. I would invite someone to add modern viewpoints, involving group theory. You can also check spires for the history of witten involvement in kaluza klein. Kaluza theory kaluzas idea three important aspects of kaluza theory. Kaluzaklein theory and extra dimensions oxford scholarship. I could only provide the original theory as understood by kaluza and klein. Einstein and the kaluza klein particle jeroen van dongen1 institute for theoretical physics, university of amsterdam valckeniersstraat 65 1018 xe amsterdam and joseph henry laboratories, princeton university princeton nj 08544 abstract in his search for a uni ed eld theory that could undercut quantum mechanics. Einstein endorsed the view of kaluza that gravity could be combined with. The original kaluzaklein theory was one of the rst attempts to create an uni ed eld theory i. Pdf kaluzaklein gravity in the context of modern embedding. The first of them is realistic kaluza klein theories.
It is a natural generalization of gauge theories which metric is just the kaluzaklein metric. Kaluza s original idea is examined and two distinct approaches to the subject are presented and contrasted. Stability of compactification of pure kaluzaklein theories. Early history of gauge theories and kaluza klein theories, with a glance at recent developments. There is almost nothing on kaluza klein theory meant for the general public. A modern kind of kaluzaklein theory is represented by the theory of a universal extra dimension. In this section, we concentrate on 5d kaluzaklein theory, which is commonly regarded as the lowenergy limit of higherdimensional theories and can be embedded in them.
A note on einstein, bergmann, and the fifth dimension, arxiv. A modern aspect that we do wish to mention, however, is the. Frw holographic dark energy cosmological model in bransdicke theory of gravitation rao, v. What is an intuitive explanation of kaluzaklein theory. I examine the relation between explanation and unification in both the original kaluzaklein theory, which originated in the works of theodor kaluza and oskar klein in the 1920s, and in the modern kaluzaklein theories which date back to the late 1970s and which are still considered by the majority of the physics community to be the best hope for a complete unified theory of all. Does kaluzaklein theory successfully unify gr and em. In the search for a unified field theory, much attention has been paid to the five dimensional analog of. Kaluza klein theories 1101 in particular for the important case of a symmetric coset space where. In physics, kaluzaklein 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. Pdf we give an elementary introduction to the kaluzaklein. Starting with the concept of spontaneous compactification, the problem of determining the ground state geometry and its symmetry is discusse. To make a connection with our fourdimensional universe we need dimensional.
Inspire, the high energy physics information system. The aim is to see what can be said about the reduction of the kaluzaklein equations rab 0 1 to the einstein equations r. A brief summary of kaluzaklein theory the physics mill. Kaluzaklein theory project gutenberg selfpublishing. In many current uni cation theories involving gravity, it is natural to add compacti ed extra dimensions. Modern kaluzaklein theories, by con trast, routinely require the addition of explicit higherdimensional matter fields in order to achieve. A scalar field and the einstein vacuum in modern kaluza klein theory paul s. Yes, if extra coordinates must be real, lengthlike and compact. Lecture 11 kaluza klein theory arindam kumar chatterjee. The description of possibility of kaluza klein theory to be the right unifying theory is.
The authors adopt the version where the whole space is a principal fiber bundle with the fourdimensional spacetime as base, and as typical. The modern formulation of differential geometry, in terms of differential forms, has. Kitchers explanatory unification, kaluza klein theories, and the normative aspect of higher dimensional unification in physics karaca, k. Kaluzaklein gravity in thecontext of modern embedding. A very elementary overview of the original kaluzaklein theory is presented, suitable for undergraduates who want to learn the basic mathematical formalism behind a revolutionary idea that was proposed one hun dred years ago, yet today serves as the template for modern higherdimensional particle and gravity theories. Thomas appelquist, alan chodos, peter george oliver freund.
The kaluzaklein theory is a shining example of einsteins unification program. Klein s unification, in particular, constitutes a type of unification which is neither reductive, nor synthetic. Actually, kaluza klein theory really has two key elements. Kitchers explanatory unification, kaluzaklein theories, and. On the geometry of kaluzaklein theories springerlink. Overduin2,3 1department of physics and astronomy, university of.
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