A representation of the quadratic Dirac equation and the Maxwell equations in terms of the three-dimensional universal complex Clifford algebra C̄3,0 is given. The investigation considers a subset of the full algebra, which is isomorphic to the Baylis algebra. The approach is based on the two Casimir operators of the Poincaré group, the mass operator and the spin operator, which is related to th...

In this paper we discuss compactness of the canonical solution operator to ∂ on weigthed L spaces on C. For this purpose we apply ideas which were used for the Witten Laplacian in the real case and various methods of spectral theory of these operators. We also point out connections to the theory of Dirac and Pauli operators.

The discrete spectrum of a q-analogue of the hydrogen atom is obtained from a deformation of the Pauli equations. As an alternative, the spectrum is derived from a deformation of the four-dimensional oscillator arising in the application of the Kustaanheimo-Stiefel transformation to the hydrogen atom. A model of the 2s−2p Dirac shift is proposed in the context of q-deformations.

We study a possibility for pseudoclassical description of a spinning particle in external electromagnetic and torsion fields. To this end we depart from the Dirac equation in such a background and derive a path integral representation for the corresponding propagator. An effective action which appears in the representation is interpreted as a pseudoclassical action for the spinning particle. It...

We study the infrared limit of two dimensional QCD, with massless dynamical Dirac fermions that are in the fundamental representation of the gauge group. We find that the theory reduces to a spin generalization of the Calogero model with an additional magnetic coupling which is of the Pauli type.

In this paper we discuss compactness of the canonical solution operator to ∂ on weigthed L spaces on C. For this purpose we apply ideas which were used for the Witten Laplacian in the real case and various methods of spectral theory of these operators. We also point out connections to the theory of Dirac and Pauli operators.

Orthonormal spin-flavor wave functions of Lorentz covariant quark models of the Bakamjian-Thomas type are constructed for nucleon resonances. Three different bases are presented. The manifestly Lorentz covariant Dirac-Melosh basis is related to the Pauli-Melosh basis and the symmetrized Bargmann-Wigner basis that are manifestly orthogonal.

The helicity amplitudes for the transitions N − S 11 and N − S 31 are presented. The amplitudes have been obtained within our front-form CQM model, based on hadron eigenstates of a relativistic mass operator and CQ current with Dirac and Pauli form factors.

• Euclid synthetic geometry 300 BC • Descartes analytic geometry 1637 • Gauss – complex algebra 1798 • Hamilton – quaternions 1843 • Grassmann – Grasmann Algebra 1844 • Cayley – Matrix Algebra 1854 • Clifford – Clifford algebra 1878 • Gibbs – vector calculus 1881 – used today • Sylvester – determinants 1878 • Ricci – tensor calculus 1890 • Cartan – differential forms 1908 • Dirac, Pauli – spin ...