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Mathematician


Apr
12
comment Interaction potential in standard $\phi^4$ theory
@QFT: you may want to post that as a more fleshed out separate follow up question. I don't have Srednicki, and I don't understand what you are asking in your edit.
Apr
11
comment Are Mathematical Physics and Occam's Razor compatible?
I migrated this from Meta, but I wonder why this question is asked at MSE and not at, say, Physics.Stackexchange...
Apr
11
comment What is the physical meaning of charges at light-like infinity in asymptotically flat space-times?
Consider an observer in Minkowski space applying a constant acceleration....
Mar
8
comment Einstein +Maxwell 's tensor
Also, this question belongs better on physics, so I am migrating it over. Please register on that site so you can edit the question into better form.
Mar
8
comment Einstein +Maxwell 's tensor
What do you mean by "Without knowing EM"? In nonlinear theories of electromagnetism your expression is manifestly false. See for example equation (7) on page 7 of arxiv.org/abs/1012.1400. If you assume you are working with Maxwell's linear theory, you have a Lagrangian formulation to which you add the Hilbert-action and assume minimal coupling to get the form above.
Feb
28
comment Cylindrical wave
One can justify this by using a little bit of differential geometry. The Laplacian term in the wave equation, using the curvilinear coordinate expression of the Laplace-Beltrami operator can be written in spherical/cylindrical symmetry in the form $r^{-\beta} \partial_r(r^{\beta} \partial_r u))$, which contains a term that looks like the logarithmic derivative $D \log f = f^{-1} Df$, and differs from the LHS of the identity I wrote down in where the "inner" $\partial_r$ sits.
Feb
28
answered Cylindrical wave
Feb
28
comment Cylindrical wave
Didn't an extremely similar question get migrated to Maths last month?
Feb
13
answered Is my electric power cord creating magnetic field when coiled?
Jan
31
comment Interaction potential in standard $\phi^4$ theory
@Qmechanic: yes yes, I welcome suggestions on other colloquial names for "change of coordinate system on the target manifold".
Jan
31
comment Interaction potential in standard $\phi^4$ theory
It is just a standard gauge transformation / change of variables. I really don't see what there is to elaborate (honest!). You graph the potential $U$, you graph the standard $\phi^4$ potential, you notice that the two potentials are exactly the same except for translations. You note that translations do not change the kinetic energy part, and voila!
Jan
31
revised Interaction potential in standard $\phi^4$ theory
added 74 characters in body
Jan
31
comment Interaction potential in standard $\phi^4$ theory
$U(\phi) = V(\psi)$ when $\psi = \phi -1$. Just plug it in.
Jan
31
answered Interaction potential in standard $\phi^4$ theory
Jan
28
comment Why don't we use quater-circular dees instead of semi-circular dees in a Cyclotron
Also, you realize that your O1 and O2 are hooked up to the same piece of metal, right? So at least as you drew it you will need to have the four oscillators timed relative to each other. Even if you remove two of the oscillators, the remaining two still need to be timed relative to each other. Unless you see somehow to get a huge benefit from this design, I guess the answer would be that the additional complication in the design is just not worth the effort.
Jan
28
comment Why don't we use quater-circular dees instead of semi-circular dees in a Cyclotron
If they are quarter circular, they'd be called $\Delta$s and not $D$s... :-) All joking aside, what is the problem you are trying to solve with the four quarter circular pieces instead of the two semicircular ones?
Jan
25
comment How is the poincare conjecture(and perelman proof) helpful in studying the properties of the universe?
A particular application: arxiv.org/abs/1204.0278
Jan
25
comment Positivity of Total Gravitational Energy in GR
en.wikipedia.org/wiki/Positive_energy_theorem
Jan
25
comment Positivity of Total Gravitational Energy in GR
@JerrySchirmer Schoen and Yau's minimal surface proof of the positive energy theory predates that of Witten's.
Jan
9
answered Einstein's equations as a Dirichlet boundary problem