Related papers: Twistor structures and boost-invariant solutions t…
Algebraically special gravitational fields are described using algebraic and differential invariants of the Weyl tensor. A type III invariant is also given and calculated for Robinson-Trautman spaces.
This is a brief overview of our work on the theory of group invariant solutions to differential equations. The motivations and applications of this work stem from problems in differential geometry and relativistic field theory. The key…
A tetrad field with spherical symmetry is applied to the charged field equations of $f(T)$ gravity theory. A special spherically-symmetric charged-dS solution is obtained. The scalar torsion of this solution is a vanishing quantity. The…
We introduce the $\theta$-twistor which is a new supersymmetric generalization of the Penrose twistor and is also alternative to the supertwistor. The $\theta$-twistor is a triple of {\it spinors} including the spinor $\theta$ extending the…
We consider a general class of scalar tensor theories in three dimensions whose action contains up to second-order derivatives of the scalar field with coupling functions that only depend on the standard kinetic term of the scalar field,…
As previously shown, the special relativistic dynamical equation of the Lorentz force type can be regarded as a consequence of a succession of space-time dependent infinitesimal Lorentz boosts and rotations. This insight indicate that the…
We take advantage of the principal bundle geometry of the space of connections to obtain general results on the presymplectic structure of two classes of (pure) gauge theories: invariant theories, and non-invariant theories satisfying two…
We discuss the structure of auxiliary fields for non-Abelian BF theories in arbitrary dimensions. By modifying the classical BRST operator, we build the on-shell invariant complete quantum action. Therefore, we introduce the auxiliary…
The Higgs field is a connection one-form as the other bosonic fields, provided one describes space no more as a manifold M but as a slightly non-commutative generalization of it. This is well encoded within the theory of spectral triples:…
It is shown that any irreducible analytic 1-flat $G$-structure as well as any analytic torsion-free affine connection with irreducibly acting holonomy group can, in principle, be contstructed by twistor methods.
We review a technique for solving a class of classical linear partial differential systems of relevance to physics in Minkowski spacetime. All the equations are amenable to analysis in terms of complex solutions in the kernel of the scalar…
We survey a new approach to the duality-invariant systems of nonlinear electrodynamics, based on introducing auxiliary bi-spinor fields. In this approach, the entire information about the given self-dual system is encoded in the U(1)…
We discuss string spectra in the low-tension limit using the BRST formalism, with emphasis on the role of triplets of totally symmetric tensors and spinor-tensors and their generalizations to cases with mixed symmetry and to (A)dS…
A certain vector-tensor (VT) theory is revisited. It was proposed and analyzed as a theory of electromagnetism without the standard gauge invariance. Our attention is first focused on a detailed variational formulation of the theory, which…
The so-called Takahashi's \emph{Inversion Theorem}, the reconstruction of a given spinor based on its bilinear covariants, are re-examined, considering alternative dual structures. In contrast to the classical results, where the Dirac dual…
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part we consider a model for spin-orbital motion: orbital…
The $sp(2M)$ invariant unfolded system is considered in the periodic twistor-like spinor space. Complete set of non-trivial charges corresponding to the global symmetry compatible with the periodicity conditions is constructed. Residual…
Tensors describing boost-invariant and cylindrically symmetric expansion of a relativistic dissipative fluid are decomposed in a suitable chosen basis of projection operators. This leads to a simple set of scalar equations which determine…
Active feedback between geometry and physics is woven throughout the study of Nature at its fundamental level, and is of key importance in string theory. Methods of complex algebraic geometry in particular have brought about an unrivaled…
In this paper I shall consider field theories in a space of four-dimensions which have field variables consisting of the components of a metric tensor and scalar field. The field equations of these scalar-tensor field theories will be…