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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282 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
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1answer
97 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
38 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 ...
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1answer
407 views

Can quantum entanglement be a proof of a 4th spatial dimension?

What I know about quantum entanglement is almost nothing. What I know can be resumed to: "two particles created together have a correlated behaviour no matter the distance between them". This is ...
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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70 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. Are ...
4
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0answers
78 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
60 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
65 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
69 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
99 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
49 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
152 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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0answers
549 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
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0answers
229 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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0answers
32 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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0answers
69 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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0answers
71 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 ...
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0answers
82 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 ...
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0answers
102 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 ...
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0answers
136 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 ...
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0answers
6 views

Velocity as the fifth dimension

In spacetime there are four general dimensions, three of space and one of time. Why is it that other dimensioned qualities seem to be rarely considered as part of spacetime? For example, why isn't ...
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0answers
23 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 ...
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69 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.
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53 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 ...
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0answers
59 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 ...
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0answers
50 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 ...