Recent content by jambaugh

I don't have a mathematical theorem in mind but I believe this is a problem with no "closed form solution". This is to say your only going to be able to calculate the field using numerical computations. I suggest you search "magnetic field software" on your favorite search engine.

The way I imagine this (quantum mechanically) is that as the magnetic field is applied the particles with magnetic moments plus spin precess but cannot change their (let's say z) component of angular momentum except by emitting/absorbing photons. These photons are then reabsorbed into the bulk...

I wish to add a few details. To formulate a relativity problem correctly, the best practice is to identify the two space-time events that define the differences which answer the questions of "how long" or "what duration" express the solution. In your example, an "observer on the train"...

I believe this should read... $$ [\epsilon^{\mu\nu\rho\sigma} M_{\mu \nu}M_{\rho\sigma},M_{\alpha\beta}]=i\epsilon^{\mu\nu\rho\sigma}(M_{\mu \nu}[M_{\rho\sigma},M_{\alpha\beta}]+[M_{\mu\nu},M_{\alpha\beta}]M_{\rho \sigma}) $$ Lie brackets obey a Leibniz rule: [AB,C] = A[B,C]+[A,C]B. In detail...

After a quick search, I now realize what you mean by "inverse bremsstralung". As I mentioned, the thermodynamics dictates that the charged particle will slow via bremsstralung radiation. However the reverse is also true if light of low entropy e.g. a laser beam interacts with charged...

Paul, You should view what you see in movies and fiction with a great deal of skepticism. Very often technical terms in physics are borrowed in order to assist in suspension of disbelief for the "magic" used in the narrative as a plot device or premise. The Lorenz force is an elementary aspect...

I don't believe you question is well formed. Note that the emission or absorption of a single photon by a charged particle is just a single term in one choice of a perturbative expansion of a total physical interaction. Take a classic (not classical [edit]) electron-electron elastic scattering...

I've seen the derivation but it has been a while. The first step is to expand the exponential into its power series which will only have two terms since the Grassmann "numbers" are nilpotent. e^{-\overline{\theta}_i A_{ij} \theta_j} = 1-\overline{\theta}_i A_{ij} \theta_j (... searching...

You should first determine the number of configurations of boys and girls that satisfy the condition, then multiply by the 4!x4! ways of rearranging the individual boys and individual girls. The number of configurations should be easily list-able. Between 2 and 10.

"just learning derivatives" in my course is, first the geometric definition as slope of tangent line on the graph of the function, then we do the limit of the difference quotient as the "formal definition". Then we start running through various properties an functions, e.g. linearity, product...

I'm teaching Calc I. this semester and we're now covering the derivatives of power function and exponential functions as well as the basic rules, e.g. linearity and product rule. Some years back I ran across an exposition of umbral calculus in the appendix of a reference. I cannot help but...

( [edit] I've cleaned up some typos.) As to the core question. \overline{\Psi} is an element of the dual space. In so far as it is a transformation you must take the Dirac adjoint of the matrix as that is what satisfies the analogue properties: D(\Lambda)^- = D(\Lambda^{-1})=D(\Lambda)^{-1}...

To understand lim sup, take a straightforward example, say: a_n = (-1)^n\frac{n}{n-1} This alternating sequence does not converge to zero, so it has no limit. In the limit, it bounces between "close to" 1 and "close to" -1. Work out ##A_n = \mathop{sup}_{k\ge n} a_k##. That will be ##a_n##...

Consider that you can always find a one-parameter abelian subgroup to the non-abelian gauge group. As we see with broken iso-spin the U(1) subgroup of the SU(2) weak isospin group manifests as a component of electric charge with the other contribution being hyper-charge. This seems to indicate...

Entanglement is not a property (observable) of the quanta. It is a characteristic of their mode of production. Certainly, the electric field quanta produced by ions will be entangled with said ions. But I am not clear on what you actually mean by having "entangled quantum properties". For a...