Abstract:
Quantization of the relativistic Hamiltonian
$H=\sqrt{c^2({\mathbf p}-{\mathbf A})^2+{(mc^2+V)}^2}+A_0$ is discussed. A new method is proposed for approximations of the corresponding path
integral. It is shown that calculation of this integral does not give the Green's function
of the Klein–Gordon equation but leads to the propagator of a scalar field in the twocomponent
Feshbach–Villars formalism. The difficulties in calculating path integrals
in the presence of nontrivial external fields are discussed.
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