Thank you, Demystifier.
I have never seen F_{\mu\nu} written like that, but using that:
F_{\mu\nu}F^{\mu\nu}=(A_{\nu\mu}-A_{\mu\nu})(A^{\nu\mu}-A^{\mu\nu})=A_{\nu\mu}A^{\nu\mu}-A_{\nu\mu}A^{\mu\nu}-A_{\mu\nu}A^{\nu\mu}+A_{\mu\nu}A^{\mu\nu}...
We can write the Born-Infeld Lagrangian as:
L_{BI}=1 - \sqrt{ 1+\frac{1}{2}F_{\mu\nu }F^{\mu\nu}-\frac{1}{16}\left(F_{\mu\nu}\widetilde{F}^{\mu\nu} \right)^{2}}
with G^{\mu\nu}=\frac{\partial L}{\partial F_{\mu\nu}} how can we show that in empty space the equations of motion take the form...
I'm sorry, i wanted to edit my post, but somehow i can't :/. That 2 obviously shouldn't be there, it was a mistake when i was writing those in latex. I was doing the math again and i think i got it. If a moderator could delete this thread that would be good. Thank you anyway haruspex.
An electric dipole p with arbitrary direction and is at distance a from plane infinite conductor at z=0.
Using the image of the dipole
##p=(2pcos\theta \hat{z}+psin\theta \hat{x}##
##p'=(2p'cos\theta \hat{z}-p'sin\theta \hat{x}##
Using the...
## \hat{A}=
\begin{pmatrix}
1 &- 1 \\
-1&1
\end{pmatrix}
##
this is written in a basis ##\left ( |1>,|2> \right )##
So, i know this is an Hermitian operator, so it can represent an observable.
Can this operator represent an electric dipole moment? A momentum? A component of the orbital angular...
Thank you, fresh_42. I'm new to the subject, things are still a little confusing.
So, we know that a ##\mathbb{M}_\mathbb{R}(4)## matrix has 16 entries, but since ##A=-A^T##, we can get rid of the elements of the upper or lower triangular part of our matrix: hence subtracting ## N(N+1)/2## from...
I am given the following set of 4x4 matrices. How can i justify that they form a basis for the Lie Algebra of the group SO(4)? I know that they must be real matrices, and AA^{T}=\mathbb{I}, and the detA = +-1. Do i show that the matrices are linearly independent, verify these properties, and...
Consider the operator Ô, choose a convenient base and obtain the representation of
\ exp{(iÔ)}
Ô =
\bigl(\begin{smallmatrix}
1 & \sqrt{3} \\
\sqrt{3} & -1
\end{smallmatrix}\bigr)
Attempt at solution:
So, i read on Cohen-Tannjoudji's Q.M. book that if the matrix is diagonal you can just...
Hey guys. So, as i was going through Griffith's Electrodynamics, and i came across this problem:
In the solutions:
How to they actually get to that expression for V = (V(bar)+vAx(bar) )Ɣ? I understand everything after that, but this just made me very confused. How do they get this from the...
Hey guys, i just came across this on my classical physics course.
So, I'm given that: E(z, t) = {E_{0}}sin(wt)sin(kz)\widehat{x}, and I'm supposed to find an expression for the associated magnetic field B.
Usually, i just find the propagation direction, and do it's cross product with the...
Homework Statement
With . Give an example, if it exists, of a non constant holomorphic function that is zero everywhere and has the form 1/n, where n € N.
Homework Equations
So.. This was in my Complex Analysis exam, and i have no idea what to do. I always seem to get stuck at these more...
I wasn't aware of that rule, thank you for pointing it out.
The intensity is the mean value of the Poynting vector. The units of the Poynting vector are W.m^-2, the same for intensity..
I can use the retation c=1/sqrt(ε0*μ0), and therefore reducing 1/cε0 = sqrt(ε0/μ0). What should i do next...