On Dirac and Pauli operators (Q1861403)

Computing the Pauli operator as the transfer operator for the Dirac operator with respect to the \(h\)-adic filtration of the spinor module, the author concludes that it coincides (up to an action of the Hodge operator) with the anticommutator of the Lie derivative along the characteristic vector field and the Hodge operator (about the action of Lie derivatives in spinor modules). Hence, the Pauli operator is a \(\mathbb{C}\)-linear operator acting on the 2D complex kernel bundle with the complex structure given by the Hodge operator. In contrast to previous construction of the Dirac operator (it is usually constructed using some connection in the spinor bundle), in this paper the Dirac and Pauli operator are obtained from the concepts based on the De Broglie principle. Moreover, the author generalizes his results to the Dirac operators acting on differential forms with values in sections of some smooth vector bundle endowed with a linear connection.