The tag has no wiki summary.

learn more… | top users | synonyms

1
vote
3answers
64 views

About constraints of the first class and electrodynamics

Let's have some theory in hamilton formalism and let's assume that it has the constraints between canonical variables $Q, \pi$. By the Dirac terminology, the set of constraints $F_{a}(Q, \pi) \approx ...
4
votes
0answers
86 views

Show that the Laplace-Runge-Lenz vector is conserved using poisson brackets

(I realise similar Phys.SE questions already exist but there is no answer with the Poisson bracket notation, I'll take this down if someone lets me know I should have commented in the existing ...
2
votes
0answers
87 views

Questions about closed forms and cycles

I read the section closed forms and cycles in Arnold's Mathematical Methods of Classical Mechanics (page 196-200), but the problems in this section is too difficult to solve in the way following the ...
2
votes
0answers
188 views

The correspondence between Poisson bracket and Commutators in Quantum Mechanics

I don't understand canonical quantization. In passing from classical to quantum, one replaces the Poisson brackets with the commutators. I don't really understand this. How can we generally show that ...
1
vote
0answers
57 views

Hamiltonian formalism in quantum electrodynamics

I need to compute $\frac{d}{dt}\hat{\mathbf P} = \frac{d}{dt}(\hat{\mathbf p} - q\hat{\mathbf A})$ for the solutions of $$ (i\gamma^{\mu}\partial_{\mu} + q\gamma^{\mu}A_{\mu} - m)\Psi = 0. $$ May I ...
0
votes
0answers
27 views

freedom of choice of 1-form in canonical representation of generic local field corresponds to gauge choice?

So it is a question in Gravitation Wheeler, Thorne and Misner 4.2 Exercise. Given F=$dp_{i}\wedge dq^{i}$. Using canonical transformation from p to $\bar{p}$ and q to $\bar{q}$, one gets ...
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 ...