In the limit [lambda] [right arrow] 0, one recovers the usual range for the canonical momentum
p [member of] (-[infinity], +[infinity]).
This, besides agreeing with the classical electron radius as well as with the canonical momentum
of a charged particle in an external field, in the sense that P = e[A.sub.tot] = eA + e[A.sub.ext] = mv + e[A.sub.ext], implies that the mass E/[c.sup.2] is of electromagnetic origin .
We use also the canonical momentum [P.sup.[mu]] [equivalent to] [p.sup.[mu]] - (e/c)[A.sup.[mu]].
In the equation which relates velocity and canonical momentum will appear the matrix :
The final expression of canonical momentum through velocity is
The final chapters discuss the exploitation of the canonical conservation law of momentum in nonlinear wave propagation, the application of canonical momentum
conservation law and material force in numerical schemes, and similarities of fluid mechanics and aerodynamics.
A Lagrangian is associated with the particle from which the canonical momentum is derived.
With reference to this Lagrangian, the canonical momentum associated with this particle is
We should obtain canonical momentum densities associated with the string as follows:
Therefore, we yield to the following canonical momentum densities:
where canonical momentum in a gravitational field is p = [m.sub.e]v(1 - 3[phi]/[c.sup.2]).
The Hamiltonian (6) can be quantized by substituting a momentum operator, [??] = -i[??][partial derivative]/[partial derivative]r, instead of canonical momentum, p.