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bio website motls.blogspot.com
location Czech Republic
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Hi, I am a string theorist and a publicist.


Jan
20
revised A dimensional regularization identity
added 79 characters in body
Jan
20
comment A dimensional regularization identity
Dear user, you should make the steps in the order I indicated. You first bring the denominator to the standard form $1/(p^2)^a$ by completing the squares. Then, with this definition of the variable $p$, you get something in the numerator whatever it is (it's a new polynomial, different from the orig. one, written in terms of $p$), and this is then treated by the second step I described which is relevant for the numerator. You seem eager to randomly permute the steps or otherwise damage the procedure I carefully sketched and then you seem to be surprised that yours doesn't work. But mine does.
Jan
20
answered At the molecular level, how is the pressure at the bottom of a lake higher than at the top?
Jan
20
answered What is a dynamical variable
Jan
19
comment relativity and aberration of light
Apologies, I probably don't understand this question of yours. If the two equations - regardless of the physical interpretations - differ by a sign, it either means that $x$ in one language means $-x$ in the other, or $c$ means $-c$ in the other, or $a$ means $\pi\pm a$ in the other, or all these three things combined. Depending on the context, some of the 4 options may be impossible.
Jan
19
comment Modification of de Donder gauge
I am pretty sure that the term $\nabla_a (\nabla_b v^b)$ which is a gradient of the divergence $\nabla\cdot v$ that you don't cancel for $n\neq 1/2$ is bad for the solvability. When the term cancels, the equations for individual components $v_a$ are pretty much independent, but they get mixed up if the term is there which probably damages the existence or uniqueness of solutions. There is a good reason why only the de Donder gauge with the right coefficient is being used but I don't have the answer in my head clearly enough to post it as a full answer.
Jan
19
answered relativity and aberration of light
Jan
19
revised relativity and aberration of light
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Jan
19
comment How many colors exist?
Dear @Ron, I agree you may be right: the Hubble-scale issues were sketched in the part of my answer about the lower limit on frequencies. For a universe with boundaries, one could indeed get a quantization of frequencies, like in a box, but with an insanely low spacing.
Jan
19
comment How many colors exist?
Dear @Zassounotsukushi, apologies if the explanation was not written clearly in my answer. I think that I wrote that the frequency is a genuinely continuous quantity but I may have failed to justify the statement. David Zaslavsky is totally right and Lorentz invariance is able to prove the continuity of the frequencies, too: nothing can change about it by quantum effects (except if one works in a box which only allows standing waves). BTW, David, a quantized Lorentz group could surely not be a usual subgroup of $SO(3,1)$ - no "dense enough" subgroup like this exists.
Jan
18
revised How many colors exist?
added 994 characters in body
Jan
18
answered How many colors exist?
Jan
18
answered A dimensional regularization identity
Jan
18
comment Modular invariance for higher genus
Hi Squark, see e.g. sciencedirect.com/science/article/pii/0370269387909464 - scholar.google.com/… - sorry for not reviewing the papers here
Jan
18
revised Why is a gaussian fixed point called gaussian?
added 41 characters in body
Jan
18
comment Why don't electromagnetic waves require a medium?
The idea that there had to be a medium for electromagnetic waves was the single most reactionary preconception that slowed down 19th century physics and many top people including Maxwell believed in this "luminiferous aether", too. They were even building models of this contrived aether out of wheels and gears. So you're not alone. Lorentz and at the end, primarily Einstein figured out that the vacuum itself may carry values of $\vec E,\vec B$ at each point and they're governed by Maxwell's equations. Visible light is an electromagnetic wave of wavelength between 350 and 700 nm or so.
Jan
18
comment Smoothness constraint of wave function
Right, there's nothing wrong about step functions, delta-functions (the derivatives of the former), and others, and that's why physicists freely work with them and never mention artificial mathematical constraints. Still, some discontinuities may make the kinetic energy infinity, so they don't exist in the finite-energy spectrum. I would add that the most natural space of functions to consider is $L^2$, all square-integrable functions. They may be Fourier-transformed or converted to other (discrete...) bases. A subset also has a finite (expectation value of) energy.
Jan
18
answered Boundary conditions / uniqueness of the propagators / Green's functions
Jan
17
comment How is this classical “paradox” resolved in electromagnetism?
Sorry, but you copied the misconception of the OP that energy is Lorentz-invariant and has to agree in all reference frames. That has led you to "solve" a paradox that never existed. Also, your detailed comments about "constraint forces" are wrong because in this experiment much like in all non-accelerated ones, constraint forces aren't doing any work.
Jan
17
answered Why is a gaussian fixed point called gaussian?