Related papers: Dirac-K\"ahler Equation (Review)
We obtain a basis of diagonal free field multi-matrix 2-point correlators in a theory with global symmetry group G. The operators fall into irreducible representations of G. This applies for gauge group U(N) at finite N. For composites made…
We present a recent work on the Dirac equation in a curved spacetime. In addition to the standard equation, two alternative versions are considered, derived from wave mechanics, and based on the tensor representation of the Dirac field. The…
Anderson's theorem asserting, that symmetry of dynamic equations written in the relativisitically covariant form is determined by symmetry of its absolute objects, is applied to the free Dirac equation. Dirac matrices are the only absolute…
We study the initial value problem of the Einstein-Dirac system, and show the stability of the Minkowski solution in the massless case with the use of generalized wave coordinates. This requires the understanding of the Dirac equation in…
Matrix and tensor formulations of the relativistic wave equation providing description both an electromagnetic field (photon) and a massless Kalb-Ramond field with the zero helicity (notoph) are given. It is shown that this equation is a…
Using superspace techniques we construct the general theory describing D=4, N=2 supergravity coupled to an arbitrary number of vector and scalar--tensor multiplets. The scalar manifold of the theory is the direct product of a special…
Extended particles are considered in terms of the fields on the Poincar\'{e} group. Dirac like wave equations for extended particles of any spin are defined on the various homogeneous spaces of the Poincar\'{e} group. Free fields of the…
We discuss from scratch the classical structure of Dirac spinors on an arbitrary globally hyperbolic, Lorentzian spacetime, their formulation as a locally covariant quantum field theory, and the associated notion of a Hadamard state.…
We systematically construct a class of two-dimensional $(2,2)$ supersymmetric gauged linear sigma models with phases in which a continuous subgroup of the gauge group is totally unbroken. We study some of their properties by employing a…
Discrete models of the Dirac-K\"{a}hler equation and the Dirac equation in the Hestenes form are discussed. A discrete version of the plane wave solutions to a discrete analogue of the Hestenes equation is established.
An equation, we call Dirac gamma-equation, is introduced with the help of the mathematical tools connected with the Clifford algebra. This equation can be considered as a generalization of the Dirac equation for the electron. Some features…
The paper considers a slightly modified one-dimensional infinite mass-in-mass chain. In the case of the long-wave approximation, which corresponds to the transition to a continuous medium, we obtained a system of two equations, which is a…
Quaternion Dirac equation has been analyzed and its supersymetrization has been discussed consistently. It has been shown that the quaternion Dirac equation automatically describes the spin structure with its spin up and spin down…
We construct a unique (2,0) supersymmetric action in six dimensions, describing a tensor multiplet interacting with a self-dual string. It is a sum of four terms: A free kinetic term for the tensor multiplet fields integrated over Minkowski…
First, the present work is concerned with generalising constructions and results in quantum field theory on curved spacetimes from the well-known case of the Klein-Gordon field to Dirac fields. To this end, the enlarged algebra of…
We investigate the semiclassical dynamics of massless Dirac fermions in 2+1 dimensions in the presence of external electromagnetic fields. By generalizing the $\alpha$ matrices to the spin-$S$ matrices and doing a certain scaling, we…
In this paper we study the Dirac field theory interacting with external gravitation field, described with tetrad of the form $e_b^\mu(x)=\varepsilon(\delta_b^\mu+\omega_{ba}^\mu x^a)$, where $\varepsilon=1$ for $\mu=0$ and $\varepsilon=i$…
We propose nonlinear Dirac equations where the conformal degree of the self-interaction terms are equal to that of the Dirac operator and the coupling parameters are dimensionless. As such, the massless equation is conformally invariant and…
It is shown that the N=4 superalgebra of the Dirac theory in Taub-NUT space has different unitary representations related among themselves through unitary U(2) transformations. In particular the SU(2) transformations are generated by the…
Applications of the Dirac equation with an anomalous magnetic moment are considered for description of characteristics of electrons, muons and quarks. The Dirac equation with four-dimensional scalar and vector potentials is reduced to a…