Related papers: Relations in Grassmann Algebra Corresponding to Th…
We present alternative postulates for Euclidean geometry whose merit is that they lead to a new class of invariants and associated geometries for real finite-dimensional unital associative algebras.
We present a consistent definition for braided ribbon networks in 3-dimensional manifolds, unifying both three and four valent networks in a single framework. We present evolution moves for these networks which are dual to the Pachner moves…
In this paper, particle physics concepts are blended into a field theory for macroscopic phenomena: Fluid mechanics is enhanced by anticommuting Grassmann variables to describe vorticity, while an additional interaction for the Grassmann…
Several classes of *-algebras associated to the action of an affine transformation are considered, and an investigation of the interplay between the different classes of algebras is initiated. Connections are established that relate…
A relation between the MacDowell-Mansouri theory of gravity and the Pontrjagin toplogical invariant in $(3+1)$ dimensions is discussed. This relation may be of especial interest in the quest of finding a mechanism to go from non-dynamical…
In the context of the integration over algebras introduced in a previous paper, we obtain several results for a particular class of associative algebras with identity. The algebras of this class are called self-conjugated, and they include,…
This paper studies nonlinear deformations of the linear gauge theory of any number of spin-2 and spin-3/2 fields with general formal multiplication rules in place of standard Grassmann rules for manipulating the fields, in four spacetime…
We work on a 4-manifold equipped with Lorentzian metric $g$ and consider a volume-preserving diffeomorphism which is the unknown quantity of our mathematical model. The diffeomorphism defines a second Lorentzian metric $h$, the pullback of…
We investigate the most general non(anti)commutative geometry in N=1 four-dimensional superspace, invariant under the classical (i.e., undeformed) supertranslation group. We find that a nontrivial non(anti)commutative superspace geometry…
In a space of d $(d > 5) $ ordinary and d Grassmann coordinates, fields manifest in an ordinary four-dimensional subspace as spinor (1/2, 3/2), scalar, vector or tensor fields with the corresponding charges, according to two kinds of…
Nonlinear analysis has played a prominent role in the recent developments in geometry and topology. The study of the Yang-Mills equation and its cousins gave rise to the Donaldson invariants and more recently, the Seiberg-Witten invariants.…
We introduce the general polynomial algebras characterizing a class of higher order superintegrable systems that separate in Cartesian coordinates. The construction relies on underlying polynomial Heisenberg algebras and their defining…
We classify all two-dimensional simple algebras (which may be non-associative) over an algebraically closed field. For each two-dimensional algebra $\mathcal{A}$, we describe a minimal (with respect to inclusion) generating set for the…
The combinatorial structure of Pachner moves in four dimensions is analyzed in the case of a distinguished move of the type (3,3) and few examples of solutions are reviewed. In particular, solutions associated to Pontryagin self-dual…
We consider configurations of lines in 3-space with incidences prescribed by a graph. This defines a subvariety in a product of Grassmannians. Leveraging a connection with rigidity theory in the plane, for any graph, we determine the…
The most general 2+1 dimensional spinning particle model is considered. The action functional may involve all the possible first order Poincare invariants of world lines, and the particular class of actions is specified thus the…
Two kinds of invariance for geometrical objects under transformations are involved in this paper. With respect to these kinds, we obtained novel invariants for almost geodesic mappings of the third type of a non-symmetric affine connection…
We construct polynomial conformal invariants, the vanishing of which is necessary and sufficient for an $n$-dimensional suitably generic (pseudo-)Riemannian manifold to be conformal to an Einstein manifold. We also construct invariants…
The Hamiltonian formulation for a non-Abelian gauge theory in two spatial dimensions is carried out in terms of a gauge-invariant matrix parametrization of the fields. The Jacobian for the relevant transformation of variables is given in…
Starting from the coadjoint Poincar\'e algebra we construct a point particle relativistic model with an interpretation in terms of extra-dimensional variables. The starting coadjoint Poincar\'e algebra is able to induce a mechanism of…