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Questions tagged [kaluza-klein]

Kaluza-Klein theory is a classical theory that unifies gravity and electromagnetism by showing that general relativity in 5-dimensions reduces to the equations of 4-dimensional general relativity and the Maxwell equations in 4 dimensions.

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Particle spectrum in dimensional reduction

First of all, sorry if this question is a bit stupid, but my knowledge of certain aspects of particle physics and group theory is a bit limited. I am compactifying the heterotic $E_{8}\times E_{8}$ ...
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Unification of gravity and electromagnetism

Have there been any attempts at unifying gravity and electromagnetism at least at classical level since Hermann Weyl's idea of gauge principle (1918)? We now have Standard Model which is very ...
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Kaluza-Klein approach and Gauss-Cadazzi approach

Can you tell me the difference or physical application of Kaluza Klein approach and Gauss Codazzi approach? In Kaluza Klein theory, 5 dimensional theory can be dimensional reduced to 4 dimensional ...
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Why Einstein's unified field theory is believed not to work?

In his later life, Albert Einstein was trying to extend his general theory of relativity to incorporate electromagnetism and other fundamental forces with it, something he himself called "The theory ...
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Lifting 3d Chern-Simons theory to 4d

For simplicity, let us only consider abelian Chern-Simons theory. The usual way of lifting 3d Chern-Simons theory to 4d is achieved through the Stokes' theorem. Say, if the original Chern-Simons ...
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What is the difficulty in extending geometrodynamics to non-abelian fields?

In an attempt to widen my own horizons I've decided to educate myself in Wheeler's Geometrodynamics. In the so-called "already unified theory" one can essentially reproduce an electromagnetic field ...
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Kaluza-Klein theory metric

What are the physical dimensions of the $5\times 5$ Kaluza-Klein metric? (the metric should be dimensionless but doesn't look so with the inclusion of the four potential and the scalar field)
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3 generations as extra unconventional dimensions?

Kaluza-Klein resonances arise in theories with extra dimensions like superstrings or old KK models. Usually, extra dimensions and KK states provide regular spacing in the spectrum. Question: can some ...
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Kaluza-Klein and Fourier expansion

In every book/reference on Kaluza-Klein (KK) dimensional reduction, one uses that fluctuations $\delta\Phi(x,y)$ can be expanded as follows $$\delta\Phi(x,y)= \sum_n\delta\Phi_n(x)\,h_n(y)$$ where $\{...
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What generates the curvature which is necessary for curling-up extra dimensions?

To say it right away, I am not an expert in string theory, but I know well General Relativity. So I wonder how the curling up of extra-dimensions which is assumed in many "Kaluza-Klein" like theories (...
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Why does Kaluza-Klein theory or the Randall-Sundrum model propose only one extra dimension?

Reading popular accounts on string theory, I have the impression that the number of extra dimensions of string theory is not an ad hoc postulate; it's uniquely determined by mathematical consistency. ...
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Attempt to understand the Kaluza-Klein theory

I'm currently doing an internship on Kaluza-Klein theory. by reading some articles, I don't understand some things that seem easy to authors for example : In this article https://arxiv.org/abs/gr-qc/...
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What is regular mass spacing?

In a book I'm reading, there is a sentence as follows: Muons and taus are not extra-dimensional versions of electrons, because they don’t have a regular mass spacing and don’t have the same weak-...
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220 views

Ricci tensor derivation in Kaluza-Klein theory

I've been trying to follow the article Kaluza-Klein for Kids where the author derives the lagrangian density in the Kaluza-Klein theory. He takes scalar function $\Phi =1$, then he uses the "ansatz" ...
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The role of the Hopf Fibration in Kaluza-Klein theory

I have been learning recently about the Hopf Fibration and its relation to physics. My professor has told me that it is one of the simplest methods of dimensional reduction in Kaluza-Klein theory. ...
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Dimensional reduction from even to odd dimensions and Chern-Simons terms

I'll be taking some Lagrangians from this paper to try and keep personal typos out of the discussion I have been looking at the dimensional reduction of Einstein-Maxwell-Dilaton theories and I am ...
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119 views

Why did Kaluza need to invent a new theory to unify general relativity and electromagnetism?

Wikipedia (and many other sources) say that by extending the number of spacetime dimensions from four to five, Kaluza–Klein theory unifies general relativity and electromagnetism into a single theory. ...
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Can someone explain the basics of Kaluza-Klein Theory (with as minimal math as possible) and why it was discredited?

Most of what I know about Kaluza-Klein Theory comes from a book I read a while back by Brian Greene called "The Elegant Universe". What he said was that Kaluza had figured out a way to incorporate a ...
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How did Einstein plan to Unify Electromagnetism and Gravity?

I'm asking the question on this site because I'm more concerned with the physics and philosophy of unification than historical details I know that Einsteins description of gravity includes curvature ...
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Massless particles in a universe with compact extra-dimensions

One common idea behind many extensions to the Standard Model (such as String Theory or Kaluza-Klein Theory) are small or hidden "Extra-Dimensions", that are compactified. According to my ...
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Why is the metric in Kaluza Klein theory set up in the way that it is?

Since the product of the electomagnetic potential with itself and the square of the radion field is added to the 4D space time metric, $$ \left( \begin{array}{ccc} g_{\mu\nu}+A_\mu A_\nu\phi^2 & \...
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268 views

If mass density curves space-time, then why isn't density (at each $x$, $y$, $z$) considered a dimension in space-time? [closed]

From http://science.howstuffworks.com "Theodor Kaluza theorized that a fourth spatial dimension might link general relativity and electromagnetic theory. But where would it go? Theoretical ...
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Kaluza-Klein in superstring theory

In superstring theory, it says that they wrap 16 dimensions on a torus given by $\mathbb{R}^{16}$ divided by a SO(32) or $E_8 \times E_8$ lattice and this gives a gauge group of the same name. But in ...
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Generalising a finding in Kaluza-Klein theory to extra spatial dimensions in super string theory a correct method?

As a disclaimer I am an A-level student. I have been doing a research project in which I am looking at manipulating space-time through the ideas provided by superstring theories. I stumbled upon the ...
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A question about Kaluza-Klein mechanism

We know that there is a kind of compactification mechanism named Kaluza-Klein theory which states that the extra dimensions can be compacted dimensions such as $T^n$ or $S^n$ and so on. To make the ...
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How To Arrive At Ground State Metric of Kaluza-Klein Theory

The ground state metric, after an extra dimension of space is compactified (to a circle) in Einsteinian gravity, is the metric which corresponds to the R_4 × S_1 geometry of the separated dimensions. ...
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The form of the metric after a dimension is compactified

Upon the compactifiation of one spatial dimension, it is said (as though an axiom) that the 5 dimensional spacetime metric separates into a 4 dimensional metric, a vector, and a scalar, (4D gravity, ...
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What does the geometry of a compactified dimension impact?

In Kaluza's original work, he didn't compactify the fifth dimension, rather imposed the "cylindrical condition" where none of the components in the 4D metric depended on the 5th dimension. It wasn't ...
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Dimensional Reduction for scalar fields

The main motivation for this question is the paper "Supersymmetric Yang-Mills Theories" by Brink, Schwarz and Scherk where they use dimensional reduction to go from Yang-Mills in $D=4$ to $D=2$. But ...
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54 views

Ground state metric?

In kaluza-klein theory, there's a notion of a "ground state metric" after compactification. What is the meaning of the term "ground state metric"?
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Doesn't modelling using Lie Groups assume spacetime is continuous?

Lie groups are used to some behaviors of quantum mechanics, as well as forming a basis for Kaluza-Klein, Yang-Mills, and String theory. But Lie groups are defined as involving a differentiable ...
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Kaluza Klein Equations of Motion

I have found a derivation of the Kaluza-Klein equations of motion on this webpage: http://www.konfluence.org/Williams_31Mar2012.pdf As I understand it, he starts with the 5d geodesic equation of ...
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Articles discussing examples of Kaluza-Klein Reduction

The notes for my class on Kaluza-Klein reduction are a bit all over the place and at times it's difficult to follow what's going on. (I plan on asking a specific question about an example later). For ...
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Momentum and Kaluza-Klein charge

In normal Kaluza Klein reduction over a $S^1$, the momentum round the circle contributes to the electric charge in the lower dimensional theory. I am curious as to whether, under certain ...
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Kaluza Klein charge

If I take a $(d+1)$ dimensional Einstein Hilbert Lagrangian $L_{d+1}=\sqrt{-\hat{g}} \hat{R}$ and perform a standard Kaluza Klein dimensional reduction by periodically identifying one direction, let's ...
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$n=0$ mode Fourier expansion on string theory

I am quite baffled at what the $n=0$ mean in compactification, why is this mode important? I mean if $n=0$ was applied here we'd just be left with I know that (39) holds from (37), but I can't ...
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What does Kaluza-Klein theory say about the attraction/repulsion of opposite/same charges?

Since Kaluza-Klein theory is made out of general relativity - a gravitational theory in 4 dimensions which is only attractive, then how does it takes into account the attraction/repulsion of opposite/...
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Regge trajectory and Kaluza Klein tower

The mass of hadrons in the Regge trajectory scales as $m=\sqrt{\frac{J}{\alpha}-\alpha_0}=\sqrt{\frac{n}{\alpha}-\alpha_0}\propto \sqrt{n}$, where $J=n$ is the spin of the particle (in natural units,...
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Lagrangian for $\mathcal{N}=4$ SQED in 3D

What is the Lagrangian for $3D$ $\mathcal{N}=4$ supersymmetric QED, with $N_f$ hypermultiplets? In particular, which is the form of the Fayet-Iliopulos terms, and the real mass terms?
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Can you compare curvatures in space, spacetime and hidden space?

Spacetime curvature is given by the cosmological constant, that produces a De-Sitter spacetime. It is non-zero. But space curvature is nearly zero (how close to zero, compared to the cosmological ...
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Is there some no-go theorem for $D=9$ Kaluza Klein QCD+EM?

While QCD is a typical product of AdS/CFT and some other research trends in extra dimensions, I have never found in the literature an example producing the non-chiral part of the standard model, ...
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162 views

Are all elementary interactions arising from a gauge theory?

The standard model of particle physics is based on the gauge group $U(1) \times SU(2) \times SU(3)$ and describes all well-known physical interactions but with exception that gravity isn't involved. ...
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Can anyone explain to a novice physicist whether there is a gravitational-electromagnetic symmetry?

I am trying to understand how the four fundamental forces relate to one another and to a theory of everything. As I understand it the unified force that is thought to exist at very high energies gets ...
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How to imagine higher dimensions?

In the link below Carl Sagan described about higher dimension: http://www.youtube.com/watch?v=UnURElCzGc0 and here's a description of Brian Greene: http://www.youtube.com/watch?v=v95WjxpMIQg Carl ...
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1answer
346 views

Ernst potential from Kaluza-Klein reduction of axisymmetric space-time

Following appendix A of "Ergoregions in Magnetised Black Hole Spacetimes" by G. W. Gibbons, A. H. Mujtaba and C. N. Pope, starting from the Lagrangian $$\mathcal{L} = \hat{R} - \hat{F}_{\mu\nu}\hat{...
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Basic question about curved and flat indices, and the Dirac matrices on $S^5$

In discussing the Kaluza-Klein formalism for Type IIB Supergravity on $S^5$, or the AdS5xS5 compactification, one requires Killing spinors on $S^5$. I read that the Dirac matrices on $S^5$ satisfy ...
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What is the significance of self-duality and anti self-duality in supergravity?

So I see the terms "self-dual" and "anti self-dual" appear routinely in supergravity/string thery, e.g. the fact that Type IIB supergravity contains a real self-dual rank-5 antisymmetric tensor $F_{\...
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$U(1)$ 5-dimensional Kaluza-Klein topological defects

Five-dimensional Kaluza-Klein theory is well-known to predict that the electromagnetic field can be described as a curled additional dimension over four-dimensional spacetime. That is, you only need ...
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Can spin angular momentum be understood as orbital angular momentum in extra dimensions?

It is to my understanding that in Kaluza-Klein theories the mass of particles can be understood as linear momentum in the extra dimensions. Let's consider in $\mathbb{R}^{1,3}\times{}B$ space-time a ...
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Justification of not quantizing small extra dimensions

When dealing with extra dimensions ($ x ^\mu $ represents $ 4D $ spacetime and $ y $ the extra dimension) we use what's known as Kaluza-Klein decomposition (basically a Fourier transform), \begin{...