Electronic Journal of Differential Equations,
Conference 04 (2000), pp. 121-145.

Title: A partial solution for Feynman's problem -
  A new derivation of the Weyl equation

Author: Atsushi Inoue (Tokyo Institute of Technology, Japan)
 
Abstract: 
Associating classical mechanics to a system of partial differential 
equations, we give a procedure for Feynman-type quantization of a 
"Schrodinger-type equation with spin." Mathematically, we construct 
a "good parametrix" for the Weyl equation with an external 
electromagnetic field. Main ingredients are (i) a new interpretation 
of the matrix structure using superanalysis and (ii) another 
interpretation of the method of characteristics as a quantization 
procedure of Feynman type.

Published July 12, 2000.
Math Subject Classifications: 35F10, 35L45, 35Q40, 70H99, 81S40.
Key Words: Quantization; good parametrix; spin; superanalysis.