In this paper I reconsider the questions of how the even-grade subalgebra of spacetime algebra can describe fermionic excitations. I start out by analyzing the content of the Pauli-ideals, i.e. the left-lorentz invariant subspaces of the even-grade subalgebra. When interpreted as rotors the general elements in that space describe massless particles with electromagnetic dipolemoments. To study t...

The Dirac particle SD is investigated by means of dynamic methods, i.e. without a use of the principles of quantum mechanics. It is shown that the Pauli particle SP and the nonrelativistic approximation SnD of the Dirac particle SD are different dynamic systems. SnD contains the high frequency degrees of freedom, which are absent in the dynamic system SP. It means that the nonrelativistic Dirac...

We derive a semiclassical time evolution kernel and a trace formula for the Dirac equation. The classical trajectories that enter the expressions are determined by the dynamics of relativistic point particles. We carefully investigate the transport of the spin degrees of freedom along the trajectories which can be understood geometrically as parallel transport in a vector bundle with SU(2) holo...

The de Broglie-Bohm causal interpretation of quantum mechanics is discussed, and applied to the hydrogen atom in several contexts. Prominent critiques of the causal program are noted and responses are given; it is argued that the de Broglie-Bohm theory is of notable interest to physics. Using the causal theory, electron trajectories are found for the conventional Schrödinger, Pauli and Dirac hy...

The Dirac particle SD is investigated by means of dynamic methods, i.e. without a use of the principles of quantum mechanics. It is shown that the Pauli particle SP and the nonrelativistic approximation SnD of the Dirac particle SD are different dynamic systems. SnD contains the high frequency degrees of freedom, which are absent in the dynamic system SP. It means that the nonrelativistic Dirac...

The classical relativistic linear AAD interaction, introduced by the author, leads in the case of weak coupling to a pointlike particle capable to be submitted to quantization via Feynman's path integrals along the line adequate to the requirements of the Pauli equation. In the discussed nonrelativistic case of the model the concept of spin is considered within early Feynman's ideas. It is know...

Using a method based on Clifford algebras taken over the reals, we present here a fully relativistic version of the Bohm model for the Dirac particle. This model is different from the one originally proposed by Bohm and Hiley and by Doran and Lasenby. We obtain exact expressions for the Bohm energy-momentum density, a relativistic quantum Hamilton-Jacobi for the conservation of energy which inc...

High approximations of semiclassical trajectory-coherent states (TCS) and of semiclassical Green function (in the class of semiclassically concentrated states) for the Dirac operator with anomalous Pauli interaction are obtained. For Schrödinger and Dirac operators trajectory-coherent representations are constructed up to any precision with respect to , → 0.

The action functional of the Standard Model of particle physics is intimately related to a specific class of first order differential operators called Dirac operators of Pauli type (“Pauli-Dirac operators”). The aim of this article is to carefully analyze the geometrical structure of this class of Dirac operators on the basis of real Dirac operators of simple type. On the basis of simple type D...