How did you guys get acclimated to the new work? Was there a lot of studying before you could actually contribute in a meaningful way? I'm not really sure how theory works.
I'm a 3rd year graduate student doing atomic physics experiment. I was thinking of changing my group to do theoretical biophysics for a few reasons. Did any experimentalist here change to theory? What was the transition like?
I was looking at the wikipedia article on CPT and it starts with "Charge, Parity, and Time Reversal Symmetry is a fundamental symmetry of physical laws under the simultaneous transformations of charge conjugation (C), parity transformation (P), and time reversal (T)."
What does it mean that CPT...
Sorry, one more clarification actually. If \gamma(\lambda) is not a vector, then what are the \gamma^{\alpha}? Are these just the coordinates? In that case wouldn't we say \gamma^\alpha = (x,y,z)^\alpha (in \mathbb{R}^3 for example) This makes it look like \gamma is a vector.
Safe, cheers lads!
I think my confusion is all cleared up. I'm still in that period of trying to forget what I know about calculus and relearn it in terms of full power differential geometry.
I have what I think is a basic question. Say I have a manifold and a metric. How do I write down the most general curve for some arbitrary parameter?
For example in \mathbb{R}^2 with the Euclidean metric, I think I should write \gamma(\lambda) = x(\lambda)\hat{x} + y(\lambda)\hat{y}
But what...
55 in my opinion is really for people who already know what they are doing and want an advanced treatment of the subject. Yes 55 does include multivariable calculus, but I wouldn't try that one unless you already knew multivariable calculus. Think of it as polishing the knowledge rather than...
Remember length contraction and time dilation do not apply to photons or any particle with a light-like spacetime interval because there does not exist a rest frame for the particle by which to relatively measure time. Boosts to light-like vectors do not rotate them in spacetime.
Photons and...
I have a different answer than what has been offered so far. I think that explaining what a particle is a very subtle question. When I'm asked I usually say something like it is an excitation of the quantum field as you said in the OP, but if you have a more mathematical background, I'd say a...
I recently thought about this. Let's say there's a hydrogen-like atom with a transition energy \omega. If it is hit with a photon of frequency \omega, it will make a transition to the excited state, so the change in internal energy is \omega. But by conservation of momentum, the atom will also...
It can be diagonalized, but usually when we diagonalize a n \times n matrix, there is some eigenbasis that we can express the n dimensional vectors it acts on. But this is strange here because the Hessian acts on scalar functions?
Several questions I have been thinking about... let me know if you have thoughts on any of them I added numbers to for coherence and readability.
So, the Hessian matrix can be used to determine the stability of critical points of functions that act on \mathbb{R}^{n}, by examining its...
Homework Statement
This is from Cahill's Physical Mathematics. Exercise 5.23.
For a \gt 0 and b^{2} – 4ac \lt 0, use a ghost contour to do the integral
\int^{\infty}_{-\infty} \frac{1}{ax^{2}+bx+c} \mathrm{d}x
Homework Equations
Use contour integration and the residue theorem...
I've found a great reference for posterity. Physical Mathematics by Cahill.
It presents topics in a succinct manner, then throws you into exercises. Every chapter could easily be read in less than a day and the exercises finished in a day or two. It has all those "little" things needed to fill...