Mostly to further my own understanding, I will explain my view of it and hope it helps.
By construction, the scalar field ##\phi## transforms under the gauge symmetry group ##SU_c(3) \times SU_L(2) \times U_Y(1)## as (1,2,1/2). That is, ##\phi## is a color singlet, ##SU_L(2)## doublet and has...
Ok, I'll just a couple of quick examples for the commutator. First, ## \epsilon^{123}=1 ## and for all cyclic permutations of {123}, and is equal to zero if any indices are repeated. It's totally antisymmetric, meaning that swapping any two indices gives a minus sign.
So, for instance ##...
## \epsilon^{ijk} ## is the Levi-Civita tensor a.k.a. the totally anti-symmetric tensor. To connect this what you have for the translation operator, ## \epsilon^{ijk} ## are the structure coefficients of the Lie Algebra group for the generators of rotation. Sorry, if I'm using to many vocab...
My understanding of it is that the graviton is said to have be spin-2 because it is described as a rank-2 tensor field. More specifically, the polarization tensor for a graviton is given by the direct product of two polarization vectors (the ones used to describe a photon field).
$$R^\mu_\nu \...
I'm not so sure as a reason there is conversation about math reform in the U.S. is due to the lack of understanding of mathematical concepts. Also, prior to HS most students have not been exposed to algebra and have zero exposure to using anything but arithmetic in physical science courses. I...
You can't use systems that are strictly non-democratic as a counterexample for whether or not education benefits a democracy.
I would say the biggest reason why replacing course like Algebra for a Citizen Math course is a bad idea is because of how negatively it impacts "mobility". As it...
Is there a paper explaining Hawking Radiation without succumbing to virtual particles similar to Jaffe's paper on the Casimir Effect? Unfortunately, Gravitation by MTW (the only GR textbook I have) doesn't cover hawking radiation and a cursory glance at google all mention pair-creation.
Or, if...
I'd say the opposite is true: there really isn't anything coherent about Copenhagen Interpretation. It's just some rules that work, but are completely at odds with the deterministic evolution of the Schrodinger equation. Though the Copenhagen Interpretation doesn't really have a set...
I think this is an interesting question that may be a bit out of my scope, but I'll try to provide at least a qualitative answer. Basically, It is not exact, but an approximation that can be justified in a regime of really weak couplings. In reality the quantum-mechanical ground state would be...
For your first part, that sounds correct: helicity for massive particles (be it fermion or boson) is not an intrinsic property and can be reversed by appropriate boosts. Just to make sure, the "handedness" of a particle in terms of helicity is something utterly different than the "handedness"...
For massive particles, it is the spin quantum number, but for massless particles, it is technically the particles helicity - i.e., the projection of spin on momentum. These two quantities are linked with the classical wave polarization. Loosely speaking, the helicity of a photon (massless...
I believe that the LHS is just the generic notation that A^\mu is undergoing a symmetry transformation. That is U just represents a certain symmetry group. In order to perform the transformation itself, you must choose a representation for that group, which in the vector representation of the...
That's for one of the Q's. What about for the other one?
Note that it's essential to make sure you have set up a clear coordinate system for the problem.