Related papers: Special generalized densities and propagators: a g…

We consider field-theoretic models, one consisting purely of scalars, the other also involving fermions, that couple to a set of constant background coupling coefficients transforming as a symmetric observer Lorentz two-tensor. We show that…

We address the recently introduced notions of generalized principal bundle and generalized principal connection by keeping track of global geometric properties through local coordinate transformation laws. This approach leads us to…

It has been found recently that propagators, e.g. the cross-correlation spectra of the cosmic fields with the initial density field, decay exponentially at large-k in an Eulerian description of the dynamics. We explore here similar…

The notion of {\it free} generalized vertex algebras is introduced. It is equivalent to the notion of {\it generalized principal subspaces} associated with lattices which are not necessarily integral. Combinatorial bases and the characters…

Co lombeau's construction of generalized functions (in its special variant) is extended to a theory of generalized sections of vector bundles. As particular cases, generalized tensor analysis and exterior algebra are studied. A point value…

A system of generalized coherent states for the de Sitter group obeying Klein-Gordon equation and corresponding to the massive spin zero particles over the de Sitter space is considered. This allows us to construct the quantized scalar…

Here we examine the propagation of relativistic fields in spacetime using the viewpoint applied to derive the Rayleigh--Sommerfeld diffraction integral in three--dimensional space. We use this theory to find the propagators for both the…

In this paper we will extend the notion of tangent bundle to a $\z$ graded tangent bundle. This graded bundle has a Lie algebroid structure and we can develop notions semi-riemannian metrics, Levi-civita connection, and curvature, on it. In…

This paper presents a generalization of symplectic geometry to a principal bundle over the configuration space of a classical field. This bundle, the vertically adapted linear frame bundle, is obtained by breaking the symmetry of the full…

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…

Distributions, i.e., subsets of tangent bundles formed by piecing together subspaces of tangent spaces, are commonly encountered in the theory and application of differential geometry. Indeed, the theory of distributions is a fundamental…

We study the generalized roundness of finite metric spaces whose distance matrix $D$ has the property that every row of $D$ is a permutation of the first row. The analysis provides a way to characterize subsets of the Hamming cube $\{ 0, 1…

In this paper, we give complex geometric descriptions of the notions of algebraic geometric positivity of vector bundles and torsion-free coherent sheaves, such as nef, big, pseudo-effective and weakly positive, by using singular Hermitian…

This paper provides two characterizations of regularity for near-vector spaces: first, by expressing them as a direct sum of vector spaces over division rings formed by distributive elements; second, by expressing their dimension in term of…

The quantum theory of the vector field minimally coupled to the gravity of the de Sitter spacetime is built in a canonical manner starting with a new complete set of quantum modes of given momentum and helicity derived in the moving chart…

In this paper we consider various notions of positivity for distributions on complex projective manifolds. We start by analyzing distributions having big slope with respect to curve classes, obtaining characterizations of generic projective…

In this work we present the foundations of generalized scalar-tensor theories arising from vector bundle constructions, and we study the kinematic, dynamical and cosmological consequences. In particular, over a pseudo-Riemannian space-time…

Considering homogeneous four-dimensional space-time geometries within real projective geometry provides a mathematically well-defined framework to discuss their deformations and limits without the appearance of coordinate singularities. On…

In this paper we present an iterative method to generate an infinite class of new nonlocal field theories whose propagators are ghost-free. We first examine the scalar field case and show that the pole structure of such generalized…

We develop a comprehensive geometric framework for defining spaces $\mathcal{G}(M,E)$ of nonlinear generalized sections of vector bundles $E \to M$ containing spaces of distributional sections $\mathcal{D}'(M, E)$. Our theory incorporates…