Questions tagged [spacetime-dimensions]

Use this tag for dimensions of a manifold, typically the space-time. DO NOT USE THIS TAG for dimension of a physical quantity nor for the size of an object.

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Double slit - higher dimensions

The double slit experiment is a real-life manifestation of the Huygens principle. As is well-known, this principle depends on whether the number of dimensions is ever or odd; as Evans1 puts it, ...
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141 views

String landscape in different dimensions

For D = 11 large (uncompactified) spacetime dimensions, the only "string theory" vacuum is M-theory For D = 10, there are 5 vacua. Or maybe it's more correct to say 4, since type I is S-dual to $Spin(...
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1k views

Upper critical dimension in field theory

Is there field theory which describe a second-order phase transition without upper critical dimension? Mermin-Wagner says something about lower critical dimension but nothing about upper dimension.
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79 views

Plum-pudding atomic physics in higher dimensions?

It is established that "normal" electron orbitals are not stable in more than 3 spatial dimensions, as the available energy levels become unbounded from below. However, this result only applies given ...
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224 views

$D$-dimensional Schrodinger's equation with a Dirac delta potential

I know that for $D\geq 2$, there is no bound state for a Dirac potential $V=-\alpha \delta(\textbf{x})$ unless we use an ultraviolet cutoff $k_{max}=1/a$. I showed this by solving the Schrodinger's ...
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1answer
470 views

Dimensional reduction of higher-dimensional Einstein-Hilbert action

I take a spacetime of the form $\mathcal{M}_{d+1}\times \mathbb{S}^n$, with $\mathcal{M}_{d+1}$ some generic non-compact $(d+1)$-dimensional spacetime and $\mathbb{S}^n$ an $n$-dimensional sphere, so ...
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85 views

Debye screening in $\mathbb{R^d}$

Consider the Poisson-Boltzmann equation $$ \nabla^2 V(r) = -\frac{1}{\epsilon_0}en\left(1 - e^{e V(r)/k_BT}\right) $$ which models the electrostatic potential in a spherically symmetric ideal gas of ...
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103 views

Are there relativistic theories with spacetime modelled on $\mathbb C^4$ rather than real Minkowski space $\mathbb R^4$?

Does anybody know of references to theories where relativity & spacetime is modelled on a (complex/Kähler) manifold which is locally diffeomorphic to $\mathbb C^4$ rather than $\mathbb R^4$, hence ...
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205 views

Structure of Hilbert Space in Bosonic String Theory

My question is about the canonical quantization of free bosonic string theory as described by Green, Schwarz & Witten. There they use spurious states to calculate a value for the ambiguity ...
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53 views

Is there an equivalent of Kaluza-Klein for fermionic dimensions?

Taking GR in $D$ dimensions, one can use the process of compactification to turn this into GR in $D-1$ dimensions coupled to a Yang-Mills field. i.e. you start with spin-2 fields and you and up with ...
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125 views

Questions about the existence of 5d & 6d version of 4d ${\cal N}=2$ SCFTs

Given a 4d N=2 Superconfomal field theory (SCFT) with a global flavor symmetry ( $\mathfrak{f}$ as the corresponding lie algebra), can we clam that this theory can always flow from a 5d ${\cal N}=1$ ...
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67 views

Hierachies of AdS/CFT holographies

One of the most disturbing aspects of General Relativity is the 'Marble versus Wood' duality of the theory: Matter creates curvature, and curvature doesn't create curvature (at least not directly) ...
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26 views

Does Birkhoff's theorem generalize to higher dimensions without additional assumptions?

In the Newtonian theory of gravity, the shell theorem says that the gravitational field inside a massive and spherically symmetric shell is zero. The conclusion is the same in general relativity, as ...
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Can one derive charged black hole solution of GR using Kaluza-Klein?

Kaluza-Klein showed that a 5 dimensional gravitional theory with one dimension on a circle, is equivalent in the limit to a 4 dimensional gravitational theory with electromagnetism. So for the ...
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86 views

Possible extra term in the Gauss-Bonnet Action

Is it possible to add a term like $\epsilon_{\alpha\beta\gamma\delta}R^{\alpha\beta}_{\enspace\mu\nu}R^{\mu\nu\gamma\delta}$ to the Gauss-Bonnet action in higher dimensional theories of gravity? Or ...
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110 views

Are there supersymmetry algebras with higher spinor representations?

The super-Poincare algebra contains supersymmetry generators $Q^I$ which satisfy fermionic anticommutation relations. By the higher-dimensional analogue of the spin-statistics theorem, they must ...
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64 views

What's the difference between internal spaces and extra dimensions?

From a geometrical perspective, we attach a copy of our gauge groups (e.g. $U(1)$ to each point in spacetime. Since Lie groups are manifolds we can, therefore, imagine that there is a little circle, ...
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218 views

Why $\kappa = 8 \pi G$ in $D$ dimensional spacetimes?

Probably another question without an answer! ;-) In most books/papers I saw on General Relativity, everybody writes $\kappa = 8 \pi G_D$ in the right part of Einstein's equation, even for spacetimes ...
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158 views

Can Higgs mechanism happen in 1+1D?

How I understand the Higgs mechanism is that, although it is called “spontaneously breaking of the gauge symmetry”, the gauge symmetry is actually not broken in the higgs mechanism and it is the ...
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306 views

The Lorentz group in three dimensions; Parity operator?

In three dimensions the Lorentz group is defined as \begin{align} \text{O}(2,1)=\{\Lambda\in\text{GL}(3,\mathbb{R}),~~~ \eta=\Lambda^T\eta\Lambda,~~~ \text{det}(\Lambda)=\pm 1\},~~~\eta=\begin{...
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328 views

Levi-Civita in 4 dimensions to 3 dimensions

i was calculating Pauli ljubanski vector in the case of massive particles . considering the rest frame(m,0,0,0) $W_i =-(m/2)\epsilon_{0ijk} M^{jk}$. I got $\epsilon_{0ijk}=\epsilon_{ijk}$. so, $W_i=-...
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166 views

Reference recommendation: QFT in arbitary dimensions $D=1+d$

When I self-study the QFT, I found that many results in textbook heavily rely on the dimension $1+3$. For example, I heard "In 3+1 dim, Majorana fermion cannot have well-defined handedness. But in ...
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93 views

If microscopic dimensions were found in particle experiments, how do we determine whether it is spatial or temporal?

This is not a question asking why our universe is 1T+3D dimensional, and hence not about how the various models such as Itzhak Bars and F theory can incoporate multiple time into a model to describe ...
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1answer
423 views

Center of mass/centroid changes between 2D and 3D?

Unless I completely botched the calculation, I noticed something strange: if you find the centroid of a 2d curve, and then revolve the curve around its axis then find the center of mass, the CM is ...
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436 views

Two dimensional spacetime and the Gauss Bonnet theorem

Generally two dimensional spacetimes are deemed to be static, as the Gauss Bonnet theorem implies that the Einstein Hilbert action would be a constant independent of $g$. But as far as I can tell, ...
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177 views

How one can write $\bar{\psi}$ in odd dimension?

I know that the Dirac equation in general dimensions has a form of $$ (i\gamma_{\mu} \nabla_\mu - m ) \psi =0 $$ and the action for that is written as $$ S = \int d^d x \bar{\psi} (i\gamma_{\mu} \...
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158 views

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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281 views

Ricci scalar higher dimensions

I was wondering if there is a straightforward way to compute the Ricci curvature of a metric that has the form (à la Kaluza-Klein): $g_{MM}\equiv\begin{pmatrix}g_{\mu\nu}&g_{\mu i}\\g_{i\nu}&...
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395 views

Bose-Einstein condensation in 3D

I have read in many books that BEC takes place in momentum space and in only 3-dimensions. What is meant by this statement?
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208 views

Relationship between lightlike and spatial compactification

The compactification of a spatial dimension, say $x^1$ given by the identification $x \sim x^1 + 2\pi R$ is said to be related to the lightlike compactification by a Lorentz boost : $$ \left( \...
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396 views

Higher dimensions

1) How we determine whether the higher dimensions are Unstable or Unpredictable? Or on the basis of what assumption we make this prediction? (Source of Image: Max Tegmark. See also this Wikipedia ...
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55 views

Are gravitons possible in 2+1 spacetime dimensions?

Spin-1 massless particles are transverse waves, so they need at least three space-time dimensions to exists. As for gravitons, I think they are still not possible in three dimensions, and to reveal ...
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33 views

How does gravity leak to other dimensions, if extra dimensions existed?

There was research article that showed the gravitational waves and electromagnetic waves propagated through the universe the same way, loosing energy by the inverse square law. The researchers ...
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39 views

Time-reversal symmetry and the generalized special axes (eg: $y$) in any $D$ space dimension

In 3D space, it is common to choose the time-reversal symmetry acting on spin-1/2 doublet fermions as $$ T = i \sigma_y K = \begin{pmatrix} 0 & 1\\ -1& 0\end{pmatrix} $$ where $K$ is complex ...
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34 views

Dimensional reduction with supermanifolds and gravity

When having compact dimensions (I guess it is not true with supermanifolds), the gravitacional constant gets diluted in extra dimensional space: $$G_N(4d)=G_N(Dd)/V(X)$$ However, I presume that the ...
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1answer
151 views

How to count degrees of freedom in a symmetric $N \times N$ matrix?

I am reading Wayne Hu's short lecture on cosmology mathematical infrastructure (https://arxiv.org/abs/astro-ph/0402060), and have several questions. Some background for us lazy people that don't want ...
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1answer
67 views

Einstein tensor in Schwarzschild spacetime

If we consider a metric in $n$-dimensional spacetime $$d s^2=-(1-f(r)) dt^2+(1-f(r))^{-1}d r^2+r^2 d\Omega_{n-2}^2,$$ what is the Einstein tensor, $G_{\mu\nu}=R_{\mu\nu}-R g_{\mu\nu}/2$, expressed in ...
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32 views

How to derive the perturbativity condition of a simple Kaluza-Klein theory?

I thought that the simple $\lambda\phi^4$ theory in 4D is always perturbative if $\lambda<1$. Below equation 107.1, PDG review of extra dimensions says that the 5D Kaluza-Klein theory $$S_5=-\int ...
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1answer
71 views

Question about quantum fields, elementary particles, and quantum numbers, and fundamental forces

As I understand it the allowable spin states of elementary particles is tied to the number of space and time dimensions, so for any two universes with the same number of space and time dimensions the ...
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1answer
58 views

'Complex dimensions' in a metric

In Special Relativity the metric is (with $\eta=\text{diag}(1, -1, -1, -1)$) $$ \text{d}s^2 = \text{d}t^2 - \text{d}\mathbf{x}^2. $$ What sets time apart from space in this equation is the "$-$" in ...
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Standard References for 5d or 6d SUSY theories?

I'd like to learn more about them, but I need a text that I know is worth reading to start!
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116 views

longitudinal and transverse components in higher dimensions

I am familiar with the Helmholz decomposition of a vector field in three dimensions: $$\vec{V}=\vec{\nabla}\wedge\vec{A}+\vec{\nabla}\phi$$ But I am interested to show that something similar can be ...
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21 views

What would it look like to be inside a small space with positive curvature?

Say you're floating in an empty void with a light source. The space you are in has a positive curvature, so going forwards will bring you back to the place you started after about 20 meters. What do ...
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64 views

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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50 views

Bound on large extra dimensions using gravitational waves

Are there proposed observations using gravitational waves which put a bound on the size of large extra dimensions (say in the context of ADD model)? The claim in the ADD paper is that you cannot ...
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84 views

Natural classification of fundamental constants of Nature

I was wondering about the fundamental constants of Nature since several years, and still pondering on them. Of course, I have read a lot of papers on them, but never found any satisfying ...
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263 views

How to best describe wave behavior on even dimensions?

Main source: http://www.mathpages.com/home/kmath242/kmath242.htm On this article, as far as I understand, the author claims that wave behavior on even dimensions would give rise to many waves with ...
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63 views

Can a 2D universe be closed?

Consider a universe as a curved 1D line looped onto itself. The second dimension is time. On one hand, this line is easy to visualize as a circle embedded in a flat 2D plane. However, there is only ...
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49 views

Multi-temporal theories: why are they no studied as space-like extra dimensions?

Beyond the initial value problem in multi-temporal wave-like equations, the existence of causality problems (we could give up if extra time directions are not too large, I think), or the instability ...
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201 views

Maximum number of dimensions in string/M-theory

M-theory low energy limit is eleven-dimensional supergravity. However I understand that Itzhak Bars and others have been working in generalizations of string theories of 12, 13 and 14 dimensions with ...