Related papers: Extended geometry and kinematics induced by biquat…
The quantum geometry arising in Loop Quantum Gravity has been known to semi-classically lead to generalizations of length-geometries. There have been several attempts to interpret these so called twisted geometries and understand their role…
Two Lagrangian functions are used to construct geometric field theories. One of these Lagrangians depends on the curvature of space, while the other depends on curvature and torsion. It is shown that the theory constructed from the first…
A new theory is considered according to which extended objects in $n$-dimensional space are described in terms of multivector coordinates which are interpreted as generalizing the concept of centre of mass coordinates. While the usual…
An extension of the General Coordinate Transformations algebra is constructed by means geometrical consistency conditions. An class of infinite invariants is derived. In particular we construct the consistent extension of the gravitational…
Kappa-Minkowski space-time is an example of noncommutative space-time with potentially interesting phenomenological consequences. However, the construction of field theories on this space, although operationally well-defined, is plagued…
We investigate the integrability of almost complex structures on the twistor space of an almost quaternionic manifold constructed with the help of a quaternionic connection. We show that if there is an integrable structure it is independent…
Considering real spacetime as a Lorentzian fiber in a complex manifold, there is a mismatch of the elementary linear representations of their symmetry groups, the real and complex Poincar\'{e} groups. No spinors are allowed as linear…
We investigate using Clifford algebra methods the theory of algebraic dotted and undotted spinor fields over a Lorentzian spacetime and their realizations as matrix spinor fields, which are the usual dotted and undotted two component spinor…
Events in Minkowski space-time can be obtained from the intersection of two twistors with no helicity. These can be represented within the geometric (Clifford) algebra formalism, in a particular conformal space that is constructed from a…
It is shown that the extended teleparallel gravitational theories, known as f(T) theories, inherit some on shell local Lorentz invariance associated with the tetrad field defining the spacetime structure. We discuss some enlightening…
In this paper we introduce the twistor space of a Riemannian manifold with an even Clifford structure. This notion generalizes the twistor space of quaternion-Hermitian manifolds and weak-Spin(9) structures. We also construct almost complex…
We discuss the possibility that spacetime geometry may be an emergent phenomenon. This idea has been motivated by the Analogue Gravity programme. These are systems where the kinematics of small perturbations are dominated by an effective…
The traditional study of plane and space algebraic curves by looking at their tangent vectors, curvatures and torsions provides geometric, but unfortunately not sufficient information about individual curves in order to be able to…
Different extended objects can fall in different ways, depending on their internal structures. Some motions are nevertheless impossible, regardless of internal structure. This paper derives universal constraints on extended-body motion,…
A simple procedure is given to construct curved, non-self-dual (complexified) Kaehler metrics on space-time in terms of deformations of holomorphic quadric surfaces in flat twistor space. Imposing Lorentzian reality conditions, the…
The formal structure of the early Einstein's Special Relativity follows the axiomatic deductive method of Euclidean geometry. In this paper we show the deep-rooted relation between Euclidean and space-time geometries that are both linked to…
The cosmological constant Lambda, which has seemingly dominated the primaeval Universe evolution and to which recent data attribute a significant present-time value, is shown to have an algebraic content: it is essentially an eigenvalue of…
We consider a length-preserving biconnection gravitational theory, inspired by information geometry, which extends general relativity by using the mutual curvature as the fundamental object describing gravity. The two connections used to…
In the loop representation the quantum constraints of gravity can be solved. This fact allowed significant progress in the understanding of the space of states of the theory. The analysis of the constraints over loop dependent wavefunctions…
Quadratic algebras are generalizations of Lie algebras; they include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical…