Reputation
Next tag badge:
96/100 score
24/20 answers
Badges
7 206 374
Newest
 fermions
Impact
~3.6m people reached

Jun
26
comment Higgs mass and the hierarchy problem
Whether you view $\Lambda^2$ divergent terms - where $\Lambda$ is a cutoff - as real ones depends on your taste. In dimensional regularization, all power-law divergences may be set to zero and only the log divergences survive. But in the previous comment, I am not talking about $\Lambda^2$ related to a cutoff but $m_{Planck}^2$ related to a particular scale, the Planck scale, where some particular objects and interactions exist and contribute. These are damn real things and the sensitivity of the Higgs on those corrections is huge regardless of the chosen regularization.
Jun
26
comment Higgs mass and the hierarchy problem
Dear @DJbunk, by dimensional analysis, it's very clear that you will get positive powers of the Planck mass in front of $h^2$. An expression like $\Delta(m^2) = C\cdot h^2/m_{Planck}$ for the Planck-physics correction to the Higgs mass has the dimension of mass so it's obviously not the right Lagrangian density, is it? So what is the mass scale you put to $C$ to get the right units of $m^4$? It may only be the Planck scale itself because that's where the source of the correction is. You will get a positive power at the end.
Jun
25
comment Higgs mass and the hierarchy problem
Dear @DJBunk, it's trivial to show that the Higgs mass is hugely affected by pretty much everything at the GUT or Planck scale unless one may show that the effect is canceled. Your $1/m_{Pl}$ coefficients appear in front of nonrenormalizable interactions induced by the Planck-scale physics, in this case. But the Higgs mass isn't a nonrenormalizable interaction. Quite on the contrary, it's a relevant term, with a positive power of mass, so $m_h^2 h^2/2$ gets corrected by terms like $M^2 h^2$ etc. where $M$ is of order the Planck mass; a correction of Planck-scale physics looks like this: huge.
Jun
25
comment Higgs mass and the hierarchy problem
In quantum field theory, the actual rules that may remove the infinitely many parameters is the scale invariance. If one requires that the theory is scale-invariant in the short-distance limit, the ultimate UV, and that's what's pretty much true for almost all consistent QFTs, this determines all the infinitely many parameters up to a finite number of them. This is the actual source of the knowledge and removal of the infinite ignorance and it requires a continuum spacetime because lattices aren't self-similar and can't produce scale-invariant theories.
Jun
25
comment Higgs mass and the hierarchy problem
Dear @Nick, there can't be any fundamental theory on a lattice or any other similar discrete background, that was really my point. You can't compute anything because all the coefficients of the non-renormalizable interactions in the continuum limit simply get translated to infinitely many terms you may construct on the lattice. And this ignorance about the infinitely many parameters is the problem, not the question whether they're hiding under the sign $\infty$. So no real problem can ever be solved by discretizing the spacetime.
Jun
25
comment Exchange operator in terms of rotation operator
This is just saying that if you attach the point 0 of a complex plane by a pushpin and you rotate the attached paper by 180 degrees around the pushpin, it will have the effect of exchanging the points "+z" and "-z". Because 2 rotations by 180 degrees act with the same sign as a single rotation by 360 degrees, one may say that the sign you get from the interchange of the particles is the same as the 360-rotation, an explanation of the spin-statistics relation that Feynman liked/invented and presented in 1986 Dirac lecture: youtube.com/watch?v=TUzI7z7bUyk&feature=related
Jun
25
answered What is the single particle Hilbert space?
Jun
25
comment Bosonic Tachyon Condensation?
Dear user, for the open strings, we actually have a description that is valid "everywhere", at distances from the perturbative vacuum that are of the same order as the order at which totally new terms start to change the behavior (eg full D-brane annihilation). For the closed strings, we don't have any string field theory that fully works so it's harder. Still, there exists neither a good description where the local minimum could be nor what it could physically mean. Bosonic string theory is simple enough to conjecture that such special structures such as new stationary points are not there...
Jun
24
answered Bosonic Tachyon Condensation?
Jun
24
comment Hierarchy is no problem and susy is a mathematical tool for data fitting
The paper is wrong. It starts with a completely wrong terminology. He says "perturbative" but he means "low-energy expansions" and he blames the hierarchy problem on this approximation. However, we may also calculate the Higgs mass etc. in the full high-energy theories (GUT and others), transcend all the "perturbative" limitations and the hierarchy problem is clearly there. See motls.blogspot.com/2012/06/… for more comments on these papers.
Jun
23
comment What is the spectrum of the Hamiltonian of the universe?
As you formulate it, the answer is very simple. The spectrum is the whole set of real non-negative numbers and the multiplicity of each eigenvalue is infinite. It's enough to realize that a single photon may move to all directions to get the infinite degeneracy for each value of the energy. The Hamiltonian effectively knows about all of dynamics in the Universe but one must go beyond the simple "spectrum and degeneracy". In particular, the spectrum of the Hamiltonian corresponds to multiparticle states and you want to know the spectum of $m^2$ of each isolated particle.
Jun
23
comment Distorted colors of Google StreetView photographs near electric power lines
Very interesting, twistor.
Jun
22
awarded  Nice Question
Jun
21
comment Distorted colors of Google StreetView photographs near electric power lines
Anna, concerning a), do you believe that some programming glitch creates a nice rainbow correlated with the shape of the tree tops and treating the R,G,B basic colors differently? I personally don't; a destruction of the picture by boxes and noise - or some color-blind fuzziness = would be much more likely. Concerning b), do you believe that in the absence of any fields, the camera sees something completely different than human eyes? Or do you believe that the people saw the color strips above the trees as well? You surely don't! ;-) Everyone would think that we had to be nuked.
Jun
21
comment Distorted colors of Google StreetView photographs near electric power lines
Very interesting, Emilio, although not a full explanation where the effect comes from. Wow, you got even to the bridge. With bikes, we've been crossing the bridge about 500 times. Isn't the halo just due to some rainbow-like effect on wet impurities covering the camera? BTW Frederic, are you sure in which direction the car was actually going?
Jun
21
comment When does a function of an operator act in the same way as the operator?
The question is trivial except that the assertion isn't true. $P_A H P_A$ may be rewritten as $p_\theta^2/a^2\cdot P_A$ which differs by $P_A$, an extra factor, from your formula. If the operator only picks the wave functions near $r=a$, you clearly can't eliminate this fact and erase $P_A$, can you? It's not enough that $r$ has already been rewritten as $a$ which is possible if it (or its function) is sandwiched between two $P_A$ operators. One still can't forget $P_A$ because $P_A\neq 1$.
Jun
21
comment Distorted colors of Google StreetView photographs near electric power lines
Sorry, the disappearance isn't supposed to be arbitrary. It's suppsoed
Jun
20
revised Distorted colors of Google StreetView photographs near electric power lines
added 283 characters in body
Jun
20
awarded  Good Question
Jun
20
asked Distorted colors of Google StreetView photographs near electric power lines