Mathematical Physics and Quantum Field Theory
Electron. J. Diff. Eqns., Conf. 04, 2000, pp. 121145.
A partial solution for Feynman's problem
 A new derivation of the Weyl equation
Atsushi Inoue
Abstract:
Associating classical mechanics to a system of partial differential
equations, we give a procedure for Feynmantype quantization
of a "Schrödingertype 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.
Mathematics Subject Classifications: 35F10, 35L45, 35Q40, 70H99, 81S40.
Key words: Quantization, good parametrix, spin, superanalysis.
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Atsushi Inoue
Department of Mathematics
Tokyo Institute of Technology
2121 Ohokayama, Meguroku
Tokyo 1520033, Japan
email: inoue@@math.titech.ac.jp 
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