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

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2
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2answers
92 views

What's the degree of freedom of this kind of matrix?

We first have a unitary matrix $$\{a_{ij}\}\quad(n\times n)$$ I know how to calculate its degree of freedom, which is $n^2$ if we consider a real variable as one degree of freedom. Now we have a ...
7
votes
1answer
242 views

Why dimensionality of the Electric Charge varies with the spacetime dimensions?

The point is: We can find via dimensional analysis that the electric charge dimensionality varies with the dimension of space-time. $$[\text{charge}] = eV^{(3-D)/2}$$(You can see below the way I did ...
1
vote
1answer
89 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 ...
0
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1answer
28 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 ...
-1
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1answer
115 views

How do we know there are dimensions above the third?

Excluding the interpretation of time being the forth dimension, what mathematical evidence is there that suggests it exists? When talking about string theory they say how there is 12 dimensions and I ...
6
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0answers
106 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 ...
4
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0answers
74 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 ...
3
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0answers
61 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} ...
3
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0answers
62 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
votes
0answers
90 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 ...
2
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0answers
47 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 ${\cal N}=1$ ...
2
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0answers
45 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
144 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
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0answers
468 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
222 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
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0answers
27 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
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0answers
62 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
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0answers
65 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
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0answers
66 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
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0answers
101 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 ...
1
vote
0answers
131 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
13 views

How can a string “shield” a tear in a flop transition? Can our expanded dimensions tear?

I have read recently that in a process called flop transition in calabi yau dimensions space actually tears and is then somehow "fixed" to create a new shape of Calabi Yau dimension. If a string wraps ...
0
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0answers
67 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
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0answers
48 views

Regarding Randall Sundrum model

In Randall Sundrum model 2, that is the one with non compact fifth dimension, there is only one brane, which is the Planck brane. The TeV brane is removed by taking the radius of the fifth dimension ...
0
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0answers
52 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
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0answers
48 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 ...