Related papers: Covariant and Contravariant Vectors
In the holomorphic or algebraic setting we consider a vector bundle E on a smooth subvariety X in a smooth variety Y over a field of characteristic zero. Assuming E extends to the l-th neighborhood of X in Y, we study cohomological…
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…
The quantization of vector bundles is defined. Examples are constructed for the well controlled case of equivariant vector bundles over compact coadjoint orbits. (Coadjoint orbits are symplectic spaces with a transitive, semisimple symmetry…
Standard practice attempts to remove coordinate influence in physics through the use of invariant equations. Trans-coordinate physics proceeds differently by not introducing space-time coordinates in the first place. Differentials taken…
Most algorithms constructing bases of finite-dimensional vector spaces return basis vectors which, apart from orthogonality, do not show any special properties. While every basis is sufficient to define the vector space, not all bases are…
We introduce the concept of bi-conformal transformation, as a generalization of conformal ones, by allowing two orthogonal parts of a manifold with metric $\G$ to be scaled by different conformal factors. In particular, we study their…
Let $n$ be a positive integer. We show that a unit rational space vector whose multiple by $n$ is an integer vector can be extended to a rational orthonormal basis whose all members have the same property.
The basic and fundamental aspects of General Relativity are in general analysed in mathematical level of coordinate basis or holonomic frame by several authors in the literature. However, for many purposes it is more convenient to use a…
Computations involving invariant random vectors are directly related to the theory of invariants (cf. e.g \cite{Weing_1}). Some simple observations along these lines are presented in this paper. We note in particular that sum of elements of…
We consider the overlap of Bethe vectors of the XXX spin chain with a diagonal twist and the modified Bethe vectors with a general twist. We find a determinant representation for this overlap under one additional condition on the twist…
We prove a vector-valued non-homogeneous Tb theorem on certain quasimetric spaces equipped with what we call an upper doubling measure. Essentially, we merge recent techniques from the domain and range side of things, achieving a Tb theorem…
In this paper we study sequences of vector orthogonal polynomials. The vector orthogonality presented here provides a reinterpretation of what is known in the literature as matrix orthogonality. These systems of orthogonal polynomials…
Orthogonal Graph Representations are essential tools for testing existence of hidden variables in quantum theory. As required by the interpretation of Copenhaghe on the foundations of quantum mechanics, a physical observable is not…
We look at generalisations of sets of vectors proving the Kochen-Specker theorem in 3 and 4 dimensions. It has been shown that two such sets, although unitarily inequivalent, are part of a larger 3-parameter family of vectors that share the…
We point out that a quantum system with a strongly positive quantum measure or decoherence functional gives rise to a vector valued measure whose domain is the algebra of events or physical questions. This gives an immediate handle on the…
Reflection and braid equations for rank two $q$-tensors are derived from the covariance properties of quantum vectors by using the $R$-matrix formalism.
A recent suggestion that vector potentials in electrodynamics (ED) are nontensorial objects under 4D frame rotations is found to be both unnecessary and confusing. As traditionally used in ED, a vector potential $A$ always transforms…
Causality imposes strong restrictions on the type of operators that may be observables in relativistic quantum theories. In fact, causal violations arise when computing conditional probabilities for certain partial causally connected…
This article presents a simple characterization for entangled vectors in a finite dimensional Hilbert space $H$. The characterization is in terms of the coefficients of an expansion of the vector relative to an orthonormal basis for $H$.…
In this letter we investigate some aspects of the noncommutative differential geometry based on derivations of the algebra of endomorphisms of an oriented complex hermitian vector bundle. We relate it, in a natural way, to the geometry of…