相关论文: Fractional residues

Let K be a henselian valued field of characteristic 0. Then K admits a definable partition on each piece of which the leading term of a polynomial in one variable can be computed as a definable function of the leading term of a linear map.…

Recent progress in quantum field theory and quantum gravity relies on mixed boundary conditions involving both normal and tangential derivatives of the quantized field. In particular, the occurrence of tangential derivatives in the boundary…

Permutation polynomials over finite fields have important applications in many areas of science and engineering such as coding theory, cryptography, combinatorial design, etc. In this paper, we construct several new classes of permutation…

In this paper we study the Frobenius characters of the invariant subspaces of the tensor powers of a representation V. The main result is a formula for these characters for a polynomial functor of V involving the characters for V. The main…

The Lagrangian formalism for tensor fields over differentiable manifolds with contravariant and covariant affine connections (whose components differ not only by sign) and metrics [$(\bar{L}_n,g)$-spaces] is considered. The functional…

We offer some elementary characterisations of group and round quadratic forms. These characterisations are applied to establish new (and recover existing) characterisations of Pfister forms. We establish "going-up" results for group and…

We study the quantum symmetric spaces for quantum general linear groups modulo symplectic groups. We first determine the structure of the quotient quantum group and completely determine the quantum invariants. We then derive the…

We construct the space of vector fields on a generic quantum group. Its elements are products of elements of the quantum group itself with left invariant vector fields. We study the duality between vector fields and 1-forms and generalize…

Relevant algebraic structures for the description of Quantum Mechanics in the Heisenberg picture are replaced by tensorfields on the space of states. This replacement introduces a differential geometric point of view which allows for a…

Fractional powers and polynomial maps preserving structured totally positive matrices, one-sided Polya frequency functions, or totally positive kernels are treated from a unifying perspective. Besides the stark rigidity of the polynomial…

A quantization procedure, which has recently been introduced for the analysis of Painlev\'e equations, is applied to a general time-independent potential of a Newton equation. This analysis shows that the quantization procedure preserves…

The paper puts together some loosely connected observations, old and new, on the concept of a quantum field and on the properties of Feynman amplitudes. We recall, in particular, the role of (exceptional) elementary induced representations…

In this short review we introduce group field theory, a particular class of random tensor models, which represents nowadays one of the candidates for a fundamental theory of quantum gravity. We insist on the combinatorial richness of…

We review the status of (scalar) quantum field theory on curved spacetimes using a novel formulation in terms of non linear functionals over the smooth configuration fields. In particular, this entails also a new foundation of locally…

We define a GL-variety to be a (typically infinite dimensional) algebraic variety equipped with an action of the infinite general linear group under which the coordinate ring forms a polynomial representation. Such varieties have been used…

A technique to linearize gravitational field equations is developed in which the perturbation metric coefficients are treated as second rank, symmetric, 1-form fields belonging to the Minkowski background spacetime by using the exterior…

The concept of permutograph is introduced and properties of integral functions on permutographs are established. The central result characterizes the class of integral functions that are representable as lattice polynomials. This result is…

There are various types of global and local spacetime invariant in general relativity. Here I focus on the local invariants obtainable from the curvature tensor and its derivatives. The number of such invariants at each order of…

This work explores the space of foliations on projective spaces over algebraically closed fields of positive characteristic, with a particular focus on the codimension one case. It describes how the irreducible components of these spaces…

We informally review the construction of spacetime geometries with multifractal and, more generally, multiscale properties. Based on fractional calculus, these continuous spacetimes have their dimension changing with the scale; they display…