Related papers: Parallel transports in tensor spaces generated by …
In this paper we explore algebraic and geometric structures that arise on parallelizable manifolds. Given a parallelizable manifold $\mathbb{L}$, there exists a global trivialization of the tangent bundle, which defines a map…
The algebra of biquaternions possess a manifestly Lorentz invariant form and induces an extended space-time geometry. We consider the links between this complex pre-geometry and real geometry of the Minkowski space-time. Twistor structures…
We study the concept of extended derivations of algebras which expands diverse definitions of generalized derivations given in the literature. We concentrate on the family of the anti-commutative algebras and classify such spaces of…
The concepts of derivations and right derivations for Leibniz algebras and $K$-B quasi-Jordan algebras naturally arise from the inner derivations determined by their algebraic structures. In this paper we introduce the corresponding…
Using the theory of extensors developed in a previous paper we present a theory of the parallelism structure on arbitrary smooth manifold. Two kinds of Cartan connection operators are introduced and both appear in intrinsic versions (i.e.,…
In this paper, we expand on previous work describing partial derivatives and metric component estimators to define tangent spaces on causal sets. Partial derivative operators are the basis vectors of the tangent space, and the metric…
We point out that the total number of trails and the total number of paths of given length, between two vertices of a simple undirected graph, are obtained as expectation values of specifically engineered quantum mechanical observables.…
The central structure in various versions of noncommutative geometry is a differential calculus on an associative algebra. This is an analogue of the calculus of differential forms on a manifold. In this short review we collect examples of…
Fractons and other subdimensional particles are an exotic class of emergent quasi-particle excitations with severely restricted mobility. A wide class of models featuring these quasi-particles have a natural description in the language of…
We construct global observable algebras and global DHR morphisms for the Virasoro minimal models with central charge c(2,q), q odd. To this end, we pass {}from the irreducible highest weight modules to path representations, which involve…
Different (not only by sign) affine connections are introduced for contravariant and covariant tensor fields over a differentiable manifold by means of a non-canonical contraction operator, defining the notion dual bases and commuting with…
We consider deformations of CFTs from the perspective of parallel transport in moduli space. In particular, we show how the deformations of individual operators can be computed and we also explore how these ideas can be extended to more…
Semigroup algebras admit certain `coherent' deformations which, in the special case of a path algebra, may associate a periodic function to an evolving path; for a particle moving freely on a straight line after an initial impulse, the wave…
We extend the construction of [19] by introducing spaces of generalized tensor fields on smooth manifolds that possess optimal embedding and consistency properties with spaces of tensor distributions in the sense of L. Schwartz. We thereby…
Probability models have been proposed in the literature to account for "intelligent" behavior in many contexts. In this paper, probability propagation is applied to model agent's motion in potentially complex scenarios that include goals…
Realizations of four dimensional Lie algebras as vector fields in the plane are explicitly constructed. Fourth order ordinary differential equations which admit such Lie symmetry algebras are derived. The route to their integration is…
A teleparallel geometry is an n-dimensional manifold equipped with a frame basis and an independent spin connection. For such a geometry, the curvature tensor vanishes and the torsion tensor is non-zero. A straightforward approach to…
The essence of the path integral method in quantum physics can be expressed in terms of two relations between unitary propagators, describing perturbations of the underlying system. They inherit the causal structure of the theory and its…
Given a submanifold $M\subset \mathbf{R}^\nu$, a curve $\gamma:I\to M$ and tangent vectors $v$ along $\gamma$, we roll the tangent space along $\gamma$. In doing so, we get an imprint/trace of $\gamma$ on the tangent space, as well as an…
The linear transport theory is developed to describe the time dependence of the number density of tracer particles in porous media. The advection is taken into account. The transport equation is numerically solved by the analytical discrete…