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.

88 questions with no upvoted or accepted answers
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14
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1answer
350 views

Link between anomalous dimensions and fractal dimensions

I just realized that anomalous dimensions in quantum/statistical field theory is not that different from fractal dimensions of objects. They both describe how quantitaive objects transform under a ...
8
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0answers
376 views

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, ...
6
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0answers
133 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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48 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 ...
5
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0answers
157 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 ...
4
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0answers
96 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 ...
4
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0answers
192 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 ...
3
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0answers
50 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 ...
3
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0answers
121 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 ${\cal N}=1$ ...
3
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0answers
64 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) ...
2
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0answers
72 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 ...
2
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70 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 ...
2
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65 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 ...
2
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139 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 ...
2
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137 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 ...
2
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0answers
234 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{...
2
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265 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=-...
2
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0answers
147 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 ...
2
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0answers
86 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 ...
2
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1answer
252 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 ...
2
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0answers
331 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, ...
2
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0answers
155 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} \...
2
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0answers
254 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}&...
2
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356 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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196 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( \...
2
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0answers
362 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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36 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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0answers
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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46 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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0answers
49 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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0answers
43 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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0answers
77 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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0answers
194 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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0answers
56 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 ...
1
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1answer
150 views

Supersymmetry beyond $D=11$ spacetime dimensions

Taking into account the higher spin theories, from which string theory is an effective field theory, I just wondering if there is something to do to extend supersymmetry to any dimension without any ...
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0answers
40 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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0answers
99 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 ...
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0answers
49 views

Compactification of spacetimes always possible?

Consider a metric in a $n+1$ dimensional spacetime given by \begin{equation} g=\underbrace{g_{tt}(r,t)dt^2 + g_{rt}(r,t)drdt + g_{rr} dr^2}_{g'} +h(t,r,x^A)dx^Adx^B \end{equation} where $h$ is a $n-1$ ...
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1answer
54 views

How to extend the notion of pressure to lower dimensional spaces?

Consider the pressure at each point in three dimensional space being given by the scalar function $P(\vec{x})$. By definition, the total force perpendicular to a given surface $S$ in this space due to ...
1
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1answer
57 views

Are there any flow to different dimension?

So far as I know from gauged supergravity there are studies of RG flows from the same dimension. Are there any flow to different dimension, i.e. flow from $AdS_5$ to $AdS_4$?
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35 views

States of equilibrium in an n-sphere

A mass at the center of two points (or a 0-sphere) that is gravitationally attracted to both would be in a state of unstable equilibrium; any disturbance would increase the attraction to one and ...
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0answers
132 views

Instability of higher dimensional universes

According to superstring theory, there are at least 10 dimensions in the universe (M-theory actually suggests that there are 11 dimensions to spacetime; bosonic string theories suggest 26 dimensions). ...
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0answers
164 views

Dimension of Representation of Majorana Fermions with Euclidean Metric?

It is possible to represent the Dirac matrices in the Majorana basis using $N= 2^{⌊d/2⌋}$-dimensional matrices, as shown here. This source uses a Minkowski metric. It would then be possible to move to ...
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1answer
81 views

Space-time dimensions

I was having a look at Seeing the fifth dimension and I was thinking the following. A dot is 0-dimensional entity. A dot "living" in an 1-dimensional world would be a moving dot along a pipe of some ...
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0answers
77 views

Can compactified dimensions enlarge and large dimensions compactify in string theory?

In string theory, can six or more dimensions rolled up into high-dimensional compact manifold become large and our 3+1 large dimensions collapse into compact manifold?
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1answer
67 views

What relative effects be for object with near light speed velocity in compactified dimensions?

What relative effects be for an object with near light speed velocity in compactified dimensions? Does gravity increase the same as for an object with near light speed velocity in usual spacial ...
1
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1answer
313 views

Does the expansion of the Universe into a higher dimensional space imply that 4D objects are real?

It is my understanding that objects in the Universe are not just getting farther apart but space itself is expanding and so in some real sense, higher-dimensional geometry is "real" -- if so, on a ...
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0answers
125 views

QFT decay rates in lower dimensions

My starting point is the decay of a Higgs particle into two fermions, with decay rate proportional to \begin{equation} \Gamma \propto g_\psi^2 N m, \end{equation} where $g_\psi$ is the coupling, $N$ ...
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0answers
136 views

The low dimensional end of the brane scan

Common wisdom says that only the top dimensional part of the brane scan of Green-Schwarz super p-brane sigma models is quantum consistent (the critical strings and the M-branes). But by the results in ...
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1answer
143 views

Is the center of the universe in another dimension?

If we live in a four dimensional world and when we try to find the center of the universe (where the big bang occured) we found that there is no apparent center, could that means that the big bang ...