Recent content by Emil_M

I would like to apply a General Lorentz Boost to some Multi-partite Quantum State. I have read several papers (like this) on the theory of boosting quantum states, but I have a hard time applying this theory to concrete examples. Let us take a ##|\Phi^+\rangle## Bell State as an example, and...

Thanks!

Hey, thanks for your reply. I will do that. Edit: since crossposting is banned, how do I delete this post?

Consider ##X## and ##Y## two vector fields on ##M ##. Fix ##x## a point in ##M## , and consider the integral curve of ##X## passing through ##x## . This integral curve is given by the local flow of ##X## , denoted ##\phi _ { t } ( p ) .## Now consider $$t \mapsto a _ { t } \left( \phi _ { t } (...

Thanks everybody for your amazing input! I will think about all the information you have given me, and might return with follow-up questions :)

Woops, you're right, that was a typo. I'm not sure I understand this. I just chose some local coordinate representation of the vector ##x##, that does not make it any less general, does it? Thank you for taking the time to help me, btw! I appreciate it.

I'm sorry, I don't understand. A basis for ## \mathbb{R}^2## needs two basis vectors. And any vector in ## \mathbb{R}^2## is then a linear combination of said basis vectors, right? Are the basis vectors of polar coordinates not given by ##\partial_r## and ##\partial_\phi##? If so, how can a...

I am really confused about coordinate transformations right now, specifically, from cartesian to polar coordinates. A vector in cartesian coordinates is given by ##x=x^i \partial_i## with ##\partial_x, \partial_y \in T_p \mathcal{M}## of some manifold ##\mathcal{M}## and and ##x^i## being some...

Thank you so much for your help! ##\lambda=\{ 2d, d, d/2, d/3,...\}## which means by ##\lambda=2\pi /k## that ## k= \{ \pi/d, 2 \pi/d, 4 \pi /d, 5 \pi/d,...\}##

Thank you for your answer! I thought if the wave consists of discrete modes, the continuous spectrum should have corresponding delta functions in order to go from integration to summation? Otherwise the dimension of the expression would change, no? I was under the impression that the canonical...

Thank you for your reply! I derived equation (2) by setting ##H_H |0>=0## with ##H_H=\int \frac{\mathrm{d} k}{2 \pi 2\omega_k}\left(A(k) A^\dagger (k)+A^\dagger (k) A(k) \right)## This Hamiltonian is derived by utelizing the Fourier transformation ##\tilde{\Phi}(k)## of ##\Phi(x)##, however, so...

Homework Statement https://i.imgur.com/sI3JiB4.jpg https://i.imgur.com/PLpnPZw.jpg I have no idea how to solve the first question about the vacuum energy. I solved the second and third problems, but I'm hopelessly stuck at the first. 2. Homework Equations The Hamiltonian can be written as...

Ah ok, the notation is introduced three pages further down... I guess this is a just a formatting error of the author Thanks for the help, though!

I came across this notation in one of my General Relativity scripts, but I checked the entire text before posting and this notation is not introduced in the script. I guess the author believes the notation is commonplace enough not to need an introduction. The only time ##D_X## was used in the...

Hi, I came across a derivation notation I didn't recognize: Let ##s## be some four-vector and ##\tau## the proper time. What is the significance of $$\frac{Ds}{\mathrm{d}\tau}?$$ I know ##Ds## can be used to mean the Jacobian, but I've never come across the notation above. Does someone...