Recent content by Heirot

Well that sounds plausible. Thanks for the answer. Can you refer me to the relevant literature?

Thinking about Newton's laws, one can see that they concern the force and the torque (the first moment of the force) acting on a particle. That is enough to describe translation and rotation. But, is there something more to this? What about second and higher moment of the force? Is there any...

It is often stated that the Kronecker delta and the Levi-Civita epsilon are the only (irreducible) invariant tensors under the Lorentz transformation. While it is fairly easy to prove that the two tensors are indeed invariant wrt Lorentz transformation, I have not seen a proof that there aren't...

For my purposes, I need a word for a quasiparticle that represents a photon in an optical medium of refractive index n. That is, a particle that travels at the speed of c/n, carries energy E and momentum p/n, where E and p are energy and momentum of a photon with the same frequency propagating...

OK, so the question is, can I identify a polariton with a particle of energy E and momentum p/n?

In vacuum, the photon has a 4-momentum (E, p) with E^2 - p^2 = 0, i.e. it's massless. However, upon entering a medium of refractive index n, we expect that the photon retains its energy, while reducing its momentum by a factor n (due to increased wavelength). We then have for the 4-momentum of a...

OK, thing are beginning to clarify... Let us first note the similarities between the four-vector of momentum P^{\mu} and four-tensor of angular momentum J^{\mu \nu}. Both have two substantially different ingredients. Symbolically we can write P^{\mu} = (E, \vec{p}) and J^{\mu \nu} = (\vec{J}...

I completely agree with you. I should rephrase my original question as: how to define J, L and S, all being four-tensors with two indices and corresponding to total, orbital and spin angular momentum, respectively, in an arbitrary frame of reference?

Can you please refer me to some literature which further discusses the imposibility of distinction between spin and orbital angular momentum in a Lorent covariant way?

I find it very strange that the total angular momentum is a 4-tensor with two indices, while the (Pauli-Lubanski) spin vector is a 4-vector when they should both transform the same way. It's like the PL spin vector carries the information about the spin of the particle as measured in its rest...

Surely you would agree that neither the electric or magnetic field are geometrically 3-vectors, yet they have well defined Lorentz transformation properties?

So, you are saying that the 1-index and 2-index description of spin are equivalent? My main concern is this: If we agree that spin should be a 3-vector in every inertial frame of reference, and we know that is is given by \vec{s} in some frame, what is the transformation property of this...

I have a problem understanding the Lorentz transformation of the spin. The spin 4-vector is defined in the rest frame of the particle as s^{\mu} = (0, \vec{s}) and then boosted in any other frame according to s'^{\mu} = (\gamma \vec{\beta} \cdot \vec{s}, \vec{s} +...

Right you are! The mystery is solved! Thank you, PAllen :)

I fail to see where the argument that the power is Lorentz invariant is used only in connection with the radiating charge. As far as I can see the argument is related to the transformation properties of energy and time and not to the radiating charge.