1
vote
0answers
21 views

How to find full energy of field of an arbitrary half-integer spin?

Let's have arbitrary half-integer spin $n + \frac{1}{2}$ representation: $$ \Psi_{\mu_{1}...\mu_{n}} = \begin{pmatrix} \psi_{a, \mu_{1}...\mu_{n}} \\ \kappa^{\dot {a}}_{\quad ...
4
votes
2answers
159 views

Hamilton formalism for Dirac spinors

Let's have the Dirac free lagrangian: $$ L = \bar {\Psi} (i\gamma^{\mu}\partial_{\mu} - m) \Psi . $$ I can rewrite it as $$ L = i\Psi^{\dagger}\partial_{0}\Psi - H_{d}, \quad H_{d} = ...
0
votes
0answers
27 views

The average value of the the square of Dirac velocity operator

Let's have Dirac velocity operator (the case of the free particle: $$ \hat {\mathbf v} = i [\hat {H}, \hat {\mathbf r}] = \hat {\alpha}, \quad \hat {H} = (\hat {\alpha} \cdot \hat {\mathbf p}) + \hat ...
0
votes
0answers
104 views

Infinitesimal transformations and Poisson bracket for Dirac spinors

I apologize for the cumbersome calculations. Let's have $\Psi$, $i\Psi^{\dagger}$, which are canonical coordinate and impulse in space of solutions of Dirac equation. It can be showed that they have ...
4
votes
3answers
487 views

Dirac equation as Hamiltonian system

Let us consider Dirac equation $$(i\gamma^\mu\partial_\mu -m)\psi =0$$ as a classical field equation. Is it possible to introduce Poisson bracket on the space of spinors $\psi$ in such a way that ...
8
votes
2answers
402 views

Dirac equation as canonical quantization?

First of all, I'm not a physicist, I'm mathematics phd student, but I have one elementary physical question and was not able to find answer in standard textbooks. Motivation is quite simple: let me ...