The ordinary Feynman-Kac-Ito formula gives a path integral representation of the Schrodinger semi-groups. We discuss here an analogous probabilistic expression for the (positive energy) solutions of the imaginary-time Klein-Gordon equation in a static external electromagnetic field. When the external field is not purely magnetic, our result is different from the path integral associated to the semi-group t is-an-element-of [0, + infinity) Bar-Arrow-Pointing-Right exp [- t(H - mc2)/hBAR] of a relativistic Schrodinger operator H = {c2[- i hBAR NABLA - (e/c) A]2 + m2c4}1/2 + V.
Imaginary-time path integrals from Klein-Gordon equation
SERVA, Maurizio
1992-01-01
Abstract
The ordinary Feynman-Kac-Ito formula gives a path integral representation of the Schrodinger semi-groups. We discuss here an analogous probabilistic expression for the (positive energy) solutions of the imaginary-time Klein-Gordon equation in a static external electromagnetic field. When the external field is not purely magnetic, our result is different from the path integral associated to the semi-group t is-an-element-of [0, + infinity) Bar-Arrow-Pointing-Right exp [- t(H - mc2)/hBAR] of a relativistic Schrodinger operator H = {c2[- i hBAR NABLA - (e/c) A]2 + m2c4}1/2 + V.File in questo prodotto:
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