Hi there,
I was wondering what is the spin of a magnetic monopole. To be specific, I mean the 't Hooft-Polyakov monopole in the Georgi-Glashow model. Sure, it is a purely classical object and as far as I know, there is no known way how to fully quantize it. So, strictly speaking, the notion...
Hi Reilly, thank you for reply.
Of course I tried to consult Google before posting my question, but maybe I didn`t try hard enough...
Exactly. As far as I understand the subject, the canonical quantization is defined by insisting on the (anti)commutation relation of the type
\{ \psi(x)...
OK, so first of all some unimportant remarks:
You are completely right. I somehow forgot that \mathcal{L} is a scalar and then hermitian == real. I also overlooked that \mathcal{L}=i\bar\psi\gamma^\mu\partial_\mu\psi is not hermitian (ie. real). Mea culpa ...
If you put t_1=-\infty and...
Hi jostpuur, thanks for interesting responses. Let me comment a bit on them:
Only the first one is popular in physics, second is ocassionaly introduced in the textbooks, but not widely used. I don't know why a Lagrangian (and consequently the action) should be real, it only has to be hermitian...
Let's have a theory involving Dirac field \psi. This theory is decribed by some Lagrangian density \mathcal{L}(\psi,\partial_\mu\psi). Taking \psi as the canonical dynamical variable, its conjugate momentum is defined as
\pi=\frac{\partial\mathcal{L}}{\partial(\partial_0\psi)}
Than the...