Recent content by UVCatastrophe

The main thing I see you're doing wrong is evaluating Feynman diagrams.

For a research project, I have to take multiple derivatives of a Yukawa potential, e.g. ## \partial_i \partial_j ( \frac{e^{-m r}}{r} ) ## or another example is ## \partial_i \partial_j \partial_k \partial_\ell ( e^{-mr} ) ## I know that, at least in the first example above, there will be a...

The reaction is X --> alpha + p + e (+ v, but we neglect) + Kinetic Energy If this is the case, then X should have the mass of the alpha+p+e+KE, slightly more than the mass of the constituents. For a contrasting situation (where a decay mode is forbidden because it weighs less than the...

Try this at home: Suppose B is moving with a speed of .6c away from A in A's rest frame. In B's rest frame, A is moving at .6c in the opposite direction away from B. They are both collaborating in an effort to observe a space-time paradox. After one year elapses in A's frame, A sends a beam...

Check for errata. Looks like they did 60 = 70a --> a = 70/60, which is wrong.

That was the first thing that came to my mind, but I think that has to do with storing the file on disk more efficiently. I think the process we are describing might be considered a type of compression, but not all compression is rescaling. For instance, some compression is lossless.

When it come to continuous symmetry operations, physics dominates in applications. I'd recommend checking out a book called An Introduction to Tensors and Group Theory for Physicists by N Jeevanjee. However, group theory finds application in many other places. Here's a computer science problem...

NP :p Yes. To test this, you could specialize to a case where a,b, and c are all orthogonal vectors of unit length. What do the triple products work out to be? You want to write x as a linear combo of a,b,c. So you need to find the coefficients lambda, mu, nu. Appealing to aforementioned...

A few terms come to mind: coarsening, rescaling, or interpolating. Don't quote me though.

Concepts The notion of linear dependence is helpful here. It might also help to review the axioms/definitions of vector spaces. Long story short, in ##D## dimensions, you need exactly ##D## vectors to provide a basis. Furthermore, all of these basis vectors must be linearly independent...

To answer your question briefly, no, the work done to lift something should not be negative. The confusion here is due to the fact that work is done by someone or something. You must ask who (or what) is doing the work? For your problem here, the formula you quote ## W_{1-2} = V_1 - V_2 ##...

This is only a partial answer, but: I'm currently in a PhD program. My university (like many others in the US) doesn't offer a masters program, only a PhD program. The PhD program is structured as follows: 1. Take two years of classes 2. After satisfying course requirements, or somewhere in...

It's a coordinate change; both ##b## and ##b'## are functions. Suppose ## f(x) = (x - a)^2 ##. What is ## f(x-a) ## ? Does ##f(x) = f(x-a)## ? If not, can you find ##g(x)## such that ##f(x-a) = g(x) ##?

Expand ## e^{ i \alpha_f \gamma_5} = 1 + i \alpha_f \gamma_5 - \frac{\alpha_f^2}{2!} \gamma_5 \ldots = \cos{\alpha_f} 1 + i \sin{\alpha_f} \gamma_5 ,## since ## \gamma_5^2 = 1##. The first term in the lagrangian goes to ##\rightarrow \bar{\psi} e^{i \alpha_f \gamma_5} ( 1 + \gamma_5 ) e^{i...

Schaum's outlines are great. Doing problems is the best way to learn physics. It's also good to have the solutions. I remember there was a Schaum's vector calculus, which started with problems on trajectories and parametrized curves and worked up to vector fields. The first physics classes you...