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May
13
comment Ten-ping bowling: Can a ping pong ball knock over a bowling pin?
Crucially, this is the speed of the ping-pong ball when it hits the pin. Given how light the ball is (compared to air density), it will need a much higher speed when being released from the hand.
May
9
comment VEV of tensor fields
@user44895: The statement holds true for any representation of the Lorentz group other than the trivial (scalar) one. But I suppose that the moment you have an anisotropic metric, you have already broken the Lorentz invariance of the field equations.
May
4
comment Is there a simple layman way to explain the incompatibilities between quantum mechanics and (general) relativity to high school students?
@brightmagus: Oh, don't worry :-) Though what I said is not incorrect, it is very (very) hand-wavy and imprecise (and some physicists might cringe). That's not the kind of statements physicists will tell each other. However, I can't think of another way to give high school students a feel for quantum gravity.
May
4
comment Definition of Information in Information Theory
Have a look at my explanation below.
May
4
comment Definition of Information in Information Theory
Here's an answer of mine. Maybe that helps. physics.stackexchange.com/a/64597/3998
Apr
29
comment Is there a way to compute (trivalent) Feynman integrals inductively from smaller diagrams?
For the diagrams you've drawn, sure. Fwiw, I tried to keep my comments fairly general.
Apr
29
comment Does Fermi-Dirac Statistics explain anti-particles?
Particles and their anti-particles both should have the same statistics -- so both bosonic or both fermionic. Bosonic examples: $\pi^{\pm}$ or $W^{\pm}$.
Apr
26
comment Finding the vacuum which breaks a symmetry
If a vacuum does not break the symmetry, then the unbroken generator must annihilate the vacuum. So the problem can be translated to finding null eigenvectors of the unbroken generators which are not null eigenvectors of the broken generators. I wonder if there is a representation theoretic argument from this point.
Apr
26
comment Scalar field divergent mass correction interpretation question (hierarchy problem)
What makes you expect higher loop corrections to cancel a large one-loop contribution? Higher loops will have answers suppressed by higher powers of the coupling and so, will be parametrically suppressed. So for small values of the coupling, how can higher order corrections save you?
Apr
21
comment Understanding Well Defined States
$H$ is the generator of time translations. So the explanation in my comment above applies to the time profile of a wavefunction $\psi(x,t)$ which is an energy eigenstate of the Hamiltonian: $H \psi(x,t) = E \psi(x,t) \implies \partial_t \psi(x,t) = E \psi(x,t)$.
Apr
21
comment Understanding Well Defined States
Naively speaking, such a wavefunction (evolution) is continuous but not not smooth, so that signals something very weird. More seriously, I think you're imagining an analog with particle in a box, whose Hamiltonian is quadratic $H = \partial_x^2$. So an oscillator over a finite duration continuously connected with "zero" wavefunction is an energy eigenstate with an eigenvalue of $-1$ i.e. a phase shift of $\pi$. On th eother hand, $H \sim \partial_t$ is not quadratic, so it shifts phase of the oscillation only by $\frac{\pi}{2}$ -- and your wavefunction is NOT an eigenstate of this operator.
Apr
20
comment How could there be a truly “pure” state?
Your question can be rephrased to: "How can there be truly isolated systems?" So the answer is the same :-)
Apr
19
comment What are threshold corrections?
@whistles: I think it might be exactly related to your infinite set of higher-dimensional operators. Each of these operators is suppressed by a suitable power of the mass scale where you've integrated out something. As you approach that mass scale (from below), you cannot truncate your calculation... but need to "resum" the full set of effective higher-dim operators. I think some such "non-perturbative" correction that happens close to a threshold scale is what the phrase refers to. A "threshold" typically refers to an energy scale where you start producing/sensing new degrees off freedom.
Apr
12
comment Can dimensional regularization solve the fine-tuning problem?
Every regulator carries an opinion about the UV physics. Intuitively, I think dimensional regularization assumes that there is no new UV physics. Further, one consistent way to compute divergent integrals is to just drop the power-law divergences, which is what dim-reg does. So it is unphysical inasmuch as you expect to see new UV physics.
Apr
12
comment why cannot fermions have non-zero vacuum expectation value?
@Paul: VEV = Vacuum expectation value i.e. a property of the vacuum. So if any object in a non-trivial representation of the Poincare algebra picks up a VEV, then some of the spacetime symmetries will be spontaneously broken by the vacuum (state). One can expect the same to apply to fluctuations around the vacuum. That would mean that the corresponding conserved quantities are not really conserved. And as far as we can see, conservation of energy-momentum and angular momentum apply quite perfectly to our universe.
Apr
12
comment why cannot fermions have non-zero vacuum expectation value?
@innisfree: In any "derivatively-coupled" theory, one cannot have a vev, right? Since there is no special point in field space.
Apr
10
comment Is $\langle k \vert k_1k_2\rangle=0$
In such a case, you'd have a 1-particle state in the initial Fock space and a 2-particle space in the final Fock space and an insertion of the time evolution operator in between them. In the case of an interacing theory with a corresponding trivalent vertex, the evolution operator can indeed cause one particle to decay into two.
Apr
10
comment Is $\langle k \vert k_1k_2\rangle=0$
In other words, a two particle state is orthogonal to a one particle state.
Apr
4
comment Dirac, Weyl and Majorana Spinors
Whoops! That was a bad slip on my part. Thanks for the correction @RobinEkman. It is indeed the direct sum.
Mar
30
comment How to conclude that an interaction is attractive from its Fourier transform (momentum space representation)?
Take a look at Anthony Zee's book: QFT in a nutshell. He explains why interactions mediated by spin 1 particles are repulsive for like charges and attractive for unlike charges, while they're the other way round for spin 0 or spin 2 mediators.