It is well known that in Dirac theory the time derivative of $P_i=p_i+A_i$ operator (where $p_i=∂/∂_i$, $A_i$ - EM field vector potential) is an analogue of the Lorentz force:
$\frac{dP_i}{dt} = e(E_i+[v×B]_i)$
On the other hand, in classical theory we have the same equation for $p_i$ instead of $P_i$. How comes that the effect of $A_i$ in Dirac theory vanishes in the classical limit?
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