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Massive spin 1/2 particles require 2-spinors for rotations, 4-spinors for rotations and boosts with parity. Including translations requires 8-spinors. Adapting 4-spinor field theory to 8-spinor fields with translation symmetry is discussed…
Dirac's equation in the field of a circularly polarized electromagnetic wave and constant magnetic field has exact localized non-stationary solutions. The solutions corresponds relativistic fermions only. Among them singular solutions with…
In two space-time dimensions a class of classical multicomponent scalar field theories with discrete, in general non-Abelian global symmetry is considered. The corresponding soliton solutions are given for the cases of 2, 3, and 4…
We construct $AdS_3\times Y_7$ solutions of type IIB supergravity, where $Y_7$ is a smooth $S^5$ bundle over a spindle $\Sigma(n_N,n_S)$, which are dual to $\mathcal{N}=(0,2)$ SCFTs in $d=2$. The solutions are constructed using the $D=5$…
We find the geometry of all supersymmetric type I backgrounds by solving the gravitino and dilatino Killing spinor equations, using the spinorial geometry technique, in all cases. The solutions of the gravitino Killing spinor equation are…
The relationship between spinors and Clifford (or geometric) algebra has long been studied, but little consistency may be found between the various approaches. However, when spinors are defined to be elements of the even subalgebra of some…
Based on the stringy differential geometry we proposed earlier, we incorporate fermions such as gravitino and dilatino into double field theory in a manifestly covariant manner with regard to O(D,D) T-duality, diffeomorphism, one-form gauge…
A system of multiple spacelike separated Dirac particles is considered and a method for constructing polynomial invariants under the spinor representations of the local proper orthochronous Lorentz groups is described. The method is a…
This paper deals with an extension of a previous work [Gravitation & Cosmology, Vol. 4, 1998, pp 107--113] to exact spherical symmetric solutions to the spinor field equations with nonlinear terms which are arbitrary functions of…
We consider bound states of fermions with an anomalous magnetic moments in the field of charged cylinder.Also we obtain second order equations for axially symmetric $Z_0(r)$-boson field, radial axially symmetric magnetic field, obtain…
A generalization of the Lagrangian introduced earlier in [2011 {\it J. Phys. G} ${\bf 37}$ 105001] for a classical color spinning particle interacting with background non-Abelian gauge and fermion fields for purpose of considering a change…
Two dimensional dilaton gravity interacting with a four-fermion model and scalars is investigated, all the coefficients of the Lagrangian being arbitrary functions of the dilaton field. The one-loop covariant effective action for 2D dilaton…
Anomalous quantization of the Electromagnetic field allows non-trivial (anti) self-dual configurations to exist in four-dimensional Euclidian space-time. These instanton-like objects are described as massless spinor particles.
Four-dimensional supersymmetric N = 1 vacua of type IIB supergravity are elegantly described by generalized complex geometry. However, this approach typically obscures the SL(2, R) covariance of the underlying theory. We show how to rewrite…
Bearing in mind the Lounesto spinor classification, we connect the expansion coefficients of well behaved fermionic quantum field, i.e., a local field within a full Lorentz covariant theory, with and only with a given subclass of Type-2…
We derive the condition on f(R) gravities that admit Killing spinor equations and construct explicit such examples. The Killing spinor equations can be used to reduce the fourth-order differential equations of motion to the first order for…
Using the language of the Geometric Algebra, we recast the massless Dirac bispinor as a set of Lorentz scalar, bivector, and pseudoscalar fields that obey a generalized form of Maxwell's equations of electromagnetism. The spinor's unusual…
The earlier proposed conditions of (bi)quaternionic differentiability are nonlinear, give rize to the 2-spinor and the self-dual gauge structures and may be considered as the it generating system of equations (GSE) with respect to the…
We study the general requirement for supersymmetric AdS$_6$ solutions in type IIB supergravity. We employ the Killing spinor technique and study the differential and algebraic relations among various Killing spinor bilinears to find the…
We develop a spinor equation of the electromagnetic field, which is equivalent to the Maxwell equation and has a similar form as the Dirac equation. The spinor is the very conjugate momentum of the vector potential in the Lagrangian…