Hello, I've found that the Faraday Tensor with both indeces down has in the first line, in MTW Gravitation book (pg 74, eq 3.7), minus the electrical field, while in Wikipedia we find that it is plus the electrical field.
Which one is right?
Does it depend on the signature of the metric?
So, thanks to your guidance, now I have proven that ##|\xi_y|<R## easily. But,
R>|\xi_y| = \frac{ |v_x| |S_z| }{ M } < \frac{ |S_z| }{ M }
because ##|v_x|<1 ## (natural units ). From there it can not be proven.
Ok, Tsny.
I've been working on this this whole week on my train trips to work, and I am not able to get it following your path. I have filled three pages and this is the best I've been able to come up with:
Fist I simplify the problem supposing that ##\vec{v}## is perpendicular to ##\vec{S}...
Oh, yes, I misunderstood the problem.
And it is a good idea to find the remaining two with the requirement that they are orthogonal to the other.
You could also use pre-calculated clebsch-gordon coefficients as scoobmx says.
In the problem statement they do not ask you to calculate the total momentum ##| J, m_j > ##. I think that you just have to write down a linear equation in the states ##|1,m_l> | 1/2, m_s > ## where ##m_l## has three possible values and ##m_s## two.
Homework Statement
Has anyone solved the part (d) of 5.6 problem of that book?
I am unable to solve it.
It asks the reader to prove that the radius ##R## of a rotating cylinder (rotating around its symmetry axis) has to be greater or equal than ##\frac{|S|}{ M } ##, in other words...