Propagators for Particles in an External Magnetic Field

Abstract

In order to describe the propagation of a scalar particle in an external potential, we begin again with the path integral

$$ K\left( {r',t';r,0} \right) = \int_{r\left( 0 \right)}^{r'\left( {t'} \right)} {\left[ {dr\left( t \right)} \right]\exp \left\{ {{\textstyle{{\rm{i}} \over \hbar }}s\left[ {r\left( t \right)} \right]} \right\}} $$

(19.1)

with

$$ S\left[ {r\left( t \right)} \right] = \int_0^{t'} {dtL\left( {r,\dot r} \right)}. $$