Graded Differential Equations and Dirac Type Operators

Author: Zilbergleit, L.V.

Source: Acta Applicandae Mathematicae, Volume 56, Number 2-3, May 1999 , pp. 301-320(20)

Publisher: Springer

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Singularities of solutions of graded differential equations as filtrations are studied. Symbols and the transfer operator associated with the h-adic filtration are computed. The condition that the transfer operator is a differential operator over the characteristic manifold of codimension 1 for this filtration is given. The Dirac operator is introduced by using the De Broglie principle: singularities of wave-like solutions move as material points. Use of the transfer operator associated with the h-adic filtration implies an invariant definition of the Pauli operator. A natural parallel translation arises as quantum analog of the Levi-Civita connection.

Keywords: De Broglie principle; Dirac operator; Pauli operator; graded differential operators; h-adic filtration; monoidal category; quantization; singularities of solutions; transfer operator

Document Type: Regular Paper

Affiliations: Golubinskaya st. 7-2, apt. 554, 117574, Moscow, Russia. email:

Publication date: May 1, 1999

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