Use this tag for dimensions of a manifold, typically the space-time. DO NOT USE THIS TAG for dimension of a physical quantity.

learn more… | top users | synonyms (1)

6
votes
4answers
133 views

Is it reasonable to visualise an additional dimension of time as a part of 4th dimensional spacetime

[EDIT] In the spirit of asking a "good question", this question is considerably more refined that the one I decided to blurt out earlier thanks to a little additional research and nudges from comments....
1
vote
3answers
75 views

Is there any experimental evidence that Universe has more than 3 spatial dimensions?

Someone asked about proof of higher dimensions. But discounting time as a dimension, along with the hyper-dimensional GUTs/Supersymmetry theories, has this possibility been tested and what did the ...
5
votes
2answers
135 views

Gravitational waves in other dimensions

I know this question is purely speculative, as we don't know if more dimensions do exist and also we do not know if gravity is indeed stronger in other dimensions (if they were to exist). But, one of ...
10
votes
1answer
295 views

Are there topological non-trivial states in zero dimension?

The periodic table of topological insulators and superconductors suggests that there can be topological non-trivial phases in zero dimension in non-interacting system with certain symmetries. A 0D ...
1
vote
1answer
44 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
vote
1answer
37 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 ...
0
votes
1answer
17 views

Ising simulation-dimensionless

My question is about dimensions in Ising model.When we want to simulate Ising we use dimensionless parameter as you know.We choose J to be 1 and also K equal 1 and when temperature is 2.26 then it's ...
0
votes
1answer
45 views

Number of supercharges in $N\ge 1$ SUSY in $d\ge4$ dimensions

I have a couple of questions concerning supercharges and superalgebras: 1, In four-dimensions, the minimal spinor representations are Weyl spinors. These have 4 real degrees of freedom (dof). This ...
0
votes
1answer
53 views

Locally accessible dimensions of configuration space

I am reading a book called "Structure and Interpretation of Classical Mechanics" by MIT Press.While discussing configuration space and degrees of freedom,the authors remark the following: Strictly ...
6
votes
0answers
113 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(...
4
votes
0answers
84 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
votes
0answers
106 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 ...
4
votes
0answers
141 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 ...
3
votes
0answers
78 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
votes
0answers
940 views

Tree level and loop level

I'm trying to read through a paper which explains the following about Universal Extra Dimensions (UED) vs ADD models: The new feature of the UED scenario compared to the brane world is that ...
2
votes
0answers
102 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
votes
0answers
93 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
votes
0answers
50 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
votes
0answers
220 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?
2
votes
0answers
261 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 ...
1
vote
0answers
31 views

How to determine the size of other galaxy's/The dark matter problem

From what i understand there are two methods (well as far as i know) to determine how much mass there is in a distant galaxy. First, Luminosity. By measuring the amount of light produced from a ...
1
vote
0answers
53 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, $N$ ...
1
vote
0answers
69 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 ...
1
vote
0answers
91 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 ...
1
vote
0answers
79 views

Are there diffrent understandings of dimensions?

If people are talking about 4 or higher dimensions they are always pictured as space dimensions. But if you have have a look at the simplest definition of a mathematical dimension it only needs to be ...
1
vote
0answers
167 views

Could a fourth dimension be “spatially simulated” one point at a time by using movements?

I wonder if time and movement can be translated into a simulation of an extra spatial dimension. At least in one point at a time. I'll try to explain. Imagine a fixed probe which measures the ...
1
vote
0answers
120 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}&...
1
vote
0answers
186 views

Folded and/or compacted dimensions in M-theory?

I've on many occasions that there are various numbers of 'extra' dimensions above the 4th. However, I've heard that they are 'compacted' or 'folded' tightly and unimaginably small. Now, as I ...
0
votes
0answers
7 views

Purpose of the multidimensional NLSE/GNLSE

I know the purpose of the NLSE (Evolution of a complex field envelope in a nonlinear dispersive medium). Usually I am solving the 1d-GNLSE when simulating the propagation of a light pulse through a ...
0
votes
0answers
42 views

Multidimensional Area and Volume

In 3D the volume is $xyz$, the product of three coordinates. But in $N$ dimension ,how to define area and volume?
0
votes
0answers
32 views

What is the relationship between potential energy and electrical potential?

I actually always thought this was trivial, now I am not so sure. For a potential $\phi$ the potential energy is $V=q\phi$ where q is a test charge. Now I am thinking this may work differently in two ...
0
votes
0answers
22 views

Compare a normal spring and a torsion spring

Consider a torsion spring with a known spring constant $K_c$. I would like to calculate the required $K_l$ for an equivalent linear spring, which would store the same amount of energy when compressed. ...
0
votes
0answers
46 views

Magnetic monopole in arbitrary dimension

Assume we have D-dimensional space-time in spherical coordinates $(t, r, \theta_1, ..., \theta_k)$. We have Maxwell equations for $k$-form $F^{\alpha_1, ..., \alpha_k}$ $$\partial_{\mu} F^{\mu \...
0
votes
0answers
37 views

Is there a limit in dimension?

According to wikipedia Dimension In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any ...
0
votes
0answers
21 views

Connecting the diffusion coefficient in 2-dimensions and 3-dimensions?

Say the diffusion coefficient of the concentration of a particle in a fluid in 3-dimensions is $D_{3\textrm{d}}$. Can we estimate the diffusion coefficient of the same particle in the same fluid, in a ...
0
votes
0answers
46 views

How confident are we that we live in a universe that has at least a 4th spatial dimension?

Modern pop culture would have us believe that there is such a thing as the 4th spatial dimension. And yes it's easily shown that $n$ dimensions is possible using math alone and 3 just happens to be ...
0
votes
0answers
26 views

Does current understanding of EM theory provide any evidence of additional physical dimensions?

Some theories (such as variants of the String Theory) postulate the existence of additional dimensions beyond the 3 spatial dimensions. So I was thinking that if such dimensions exist, perhaps some ...
0
votes
0answers
115 views

How do these 3D paintings work ? (See the images)

I know that our brain perceives two images from two eyes and combine them to see 3 dimensions and the 3D stuff uses this. But how this works and how can there be two images ? Thanks in advance :)
0
votes
0answers
98 views

Topology of a black hole

How many dimensions are theorized for a black hole, in view of the fact that black holes are not observed directly.
0
votes
0answers
75 views

Compactification and off-diagonal terms of the metric tensor

In standard 3+1 dimensional spacetime, the metric tensor is of order 4 and had ten independent coefficients, hence there are 6 terms off the diagonal in the corresponding $4\times 4$ real symmetric ...
0
votes
0answers
56 views

how must i understand this 2-loop integral?

let be the 2-loop integral... $$ \int d^{d}l\int d^{d}k \frac{1}{k^{4}(k+p)^{2}(k+l)^{2}}=I(p)$$ dimensional regularization over the variable 'l0 to evaluate $$ \int d^{d}l\frac{1}{(k+l)^{2}}=G(k,d)...