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We introduce the new, exactly solvable model of the two-dimensional Dirac fermion in presence of an asymmetric, P\"oschl-Teller-like vector potential. Utilizing the translation invariance of the system, the effective one-dimensional…
We study the theory of systems with constraints from the point of view of the formal theory of partial differential equations. For finite-dimensional systems we show that the Dirac algorithm completes the equations of motion to an…
Quark-meson duality for two-point functions of vector and axial-vector QCD currents is investigated in the large-Nc approximation. We find that the joint constraints of duality and chiral symmetry imply degeneracy of excited vector and…
The Kerr spinning particle has a remarkable analytical twistorial structure. Analyzing electromagnetic excitations of the Kerr circular string which are aligned to this structure, we obtain a simple stringy skeleton of the spinning particle…
Classes of relativistic symmetries accommodating supersymmetric patterns are considered for the Dirac Hamiltonian with axially-deformed scalar and vector potentials.
Ideas from deformation quantization are applied to deform the expression of elements of an algebra. Extending these ideas to certain transcendental elements implies that $\frac{1}{i\h}uv$ in the Weyl algebra is naturally viewed as an…
The property of cyclicity of a linear operator, or equivalently the property of simplicity of its spectrum, is an important spectral characteristic that appears in many problems of functional analysis and applications to mathematical…
There suggested a modification of the Dirac electron theory, eliminating its mathematical incompleteness. The modified Dirac electron, called dual, is described by two waves, one of which is the Dirac wave and the second dynamically…
We show that the Dirac factorization method can be successfully employed to treat problems involving operators raised to a fractional power. The technique we adopt is based on an extension of the Pauli matrices and the properties of the…
We explore the Dirac equation in external electromagnetic and torsion fields. Motivated by the previous study of quantum field theory in an external torsion field, we include a nonminimal interaction of the spinor field with torsion. As a…
Representations of Dirac-Hestenes and Dirac spinor fields via coordinates of surfaces conformally immersed into 4-dimensional complex space are proposed. A relation between time evolution of spinor fields and integrable deformations of…
The aim of this work is to find exact solutions of the Dirac equation in 1+1 space-time beyond the already known class. We consider exact spin (and pseudo-spin) symmetric Dirac equations where the scalar potential is equal to plus (and…
We define and study the probability current and the Hamiltonian operator for a fully general set of Dirac matrices in a flat spacetime with affine coordinates, by using the Bargmann-Pauli hermitizing matrix. We find that with some weak…
A description of elementary particles should be based on irreducible representations of the Poincar\'e group. In the theory of massive representations of the full Poincar\'e group there are essentially four different cases. One of them…
We consider propagating torsion as a completion of gravitation in order to describe the dynamics of curved-twisted space-times filled with Dirac spinorial fields; we discuss interesting relationships of the torsion axial vector and the…
A Lagrangian theory giving rise to a version of the Dirac-Kahler equations on curved backgrounds is considered. The principal pieces are the general fields which have values in the algebra of the Dirac matrices and satisfy a Dirac-type…
The problem of a fermion subject to a general scalar potential in a two-dimensional world for nonzero eigenenergies is mapped into a Sturm-Liouville problem for the upper component of the Dirac spinor. In the specific circumstance of an…
The properties of Dirac gamma matrices in a four-dimensional space-time with the $(2,2)$ signature are studied. The basic spinors are classified, and the existence of Majorana-Weyl spinors is noted. Supersymmetry in $2 + 2$ dimensions is…
The spectral torsion is defined by three vector fields and Dirac operators and the noncommutative residue. Motivated by the spectral torsion and the one form rescaled Dirac operator, we give some new spectral torsion which is the extension…
We discuss how basic Clifford algebra and indeed all of matrix algebra and matrix representations of finite groups comes from Iterants: very elementary processes such as an alternation of plus and minus one ...+-+-+- .... One can think of…