Recent content by odietrich

Thanks for your suggestions! I'm currently trying to find out how to learn from these about Casimir operators as well as the central charge (is this the same as the central extension defined by Barut and Raczka?) and the Galilei group. A first quick search yielded nothing about central charges...

Could you (@vanhees71) or anyone else kindly point to some text(book) with a physicist-friendly introduction to those aspects or Lie groups/algebras that are mentioned above (i.e., definition of the central charge and Casimir operators as well as the application to the Poincaré and Galilei...

A ##90°_x## RF pulse acts on the magnetization ##\mathbf{M}=(M_x,M_y,M_z)^T## as a ##90°## rotation matrix ##\mathsf{R}## (around the ##x## axis) with $$\mathsf{R}=\begin{pmatrix}1&0&0\\0&0&-1\\0&1&0\end{pmatrix}$$ i. e. the magnetization vector is rotated by ##90°## around the ##x## axis. The...

The direction can change, but it's one of the basic (and not really intuitive) properties of elementary particles that the magnitude of the spin cannot change. So, if we use for a moment the (at least inaccurately simplified, and physicists would generally use the word "wrong") model of a tiny...

Here's a solution (took some staring:smile:): $$s_1 = s_6 + s_3 (\frac{s_2}{s_5} - \frac{s_5}{s_2})$$ and $$s_4 = s_6 + s_5 (\frac{s_2}{s_3} - \frac{s_3}{s_2}).$$ With this solution, I can express ##s_1## and ##s_4## by the matrix entries ##s_2, s_3, s_5##, and ##s_6##. So, if the symmetric...

Considering Orodruin's suggestion in more detail, I found that I can write the symmetric matrix ##\textbf{S}=\begin{pmatrix}s_1&s_2&s_3\\s_2&s_4&s_5\\s_3&s_5&s_6\end{pmatrix}## as ##v\textbf{1} + (u-v) (\textbf{v}_1\otimes\textbf{v}_1) = v\textbf{1} + (u-v)...

Thanks for your suggestion! I think that the resulting parameters are very similar to another set of 4 numbers (that I had considered before, but didn't mention in my question above): the eigenvector of ##a## multiplied by ##a## and the eigenvalue ##b##? I tried least-squares fitting with these...

I'm looking for the general form of a symmetric 3×3 matrix (or tensor) ##\textbf{A}## with only two different eigenvalues, i.e. of a matrix with the diagonalized form ##\textbf{D}=\begin{pmatrix}a& 0 & 0\\0 & b & 0\\0 & 0 & b\end{pmatrix} = \text{diag}(a,b,b)##. In general, such a matrix can be...