Dimensional analysis means to obtain results by analyzing the units in question, etc. DO NOT USE THIS TAG if your question is about degrees of freedom or spatial dimensions.

learn more… | top users | synonyms

19
votes
1answer
365 views

Mass of empty AdS$_5$

Five dimensional empty AdS$_5$ space has mass $$ E = \frac{3 \pi \ell^2}{32 G}. $$ Is the above equation correct? Let's do some dimensional analysis to confirm. In natural units, in 5 dimensions ...
4
votes
1answer
56 views

Dimension agreement in canonical transformation

In this Physics.SE post, there is a transformation: $$Q = q,$$ $$P = \sqrt{p} - \sqrt{q}.$$ for Hamiltonian $H = \frac{p^2}{2}$. The post discusses the validity of this transformation as a canonical ...
0
votes
1answer
32 views

Formula for Electrical Arc Length

I was playing with some High-Voltage the other day, when a question popped into my head. Can you calculate length of an electrical arc? It probably would be proportional to :- 1. Voltage of the source ...
6
votes
0answers
154 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 ...
3
votes
0answers
141 views

Can mass dimension of a field be viewed as another 'quantum number'?

While studying SUSY in 4D, I noticed the dynamical chiral superfield has dimension [GeV], whereas the dynamical vector superfield (for gauge theories) is unitless. Because I was introduced to the ...
2
votes
0answers
239 views

What prediction led to the vacuum catastrophe?

The disagreement between predicted and measured energy density of the vacuum is one of the great unsolved problems of science. According to this book the predicted energy density was obtained as ...
2
votes
0answers
193 views

Dimensional analysis to estimate order of magnitude of quantities

In the Coursera course From the Big Bang to Dark Energy on several occasions dimensional analysis was used to estimate the scale of quantities. This almost seems like a contradiction in terms to me, ...
2
votes
0answers
44 views

Scaling in Vlasov equations

This question is in reference to the paper, http://arxiv.org/abs/1301.7182 What exactly is the argument being made on page 6 and 7? One deduces that the function $\Delta$ has to be such that, ...
1
vote
0answers
22 views

Quantum Efficiency Estimation

Might there be a way to do a rough estimate of the quantum efficiency of a photo-detector like a CCD or CMOS sensor based only on a picture taken with it? I've read papers and guides (like this one: ...
1
vote
0answers
125 views

Scale-invariant differential operator

For example, the differential operator Laplacian is $$\nabla^2 = \frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}.$$ My questions are: Is it scale-invariant? what is ...
1
vote
0answers
46 views

How to determine that the renormalization constant $Z_3$ must depend only on $g$ and $\Lambda/m$

In Le Bellac's book, Quantum and Statistical Field Theory, the renormalization constant $Z_3$ is introduced with the equation $$ \Gamma^{(2)}_R(k^2, m^2, g) = Z_3 \Gamma^{(2)}(k^2, m_0^2, g_0; ...
0
votes
0answers
30 views

Justifying order of magnitude reasoning

So in the context of a set of notes I am reading about acoustics I get to equation (23) in this paper. Basically it comes down to showing that (note the dots above the a's meaning time derivative!) ...