Related papers: Bosonic Laplacians in higher spin Clifford analysi…
Second-order polynomials generalize classical first-order ones in allowing for additional variables that range over functions rather than values. We are motivated by their applications in higher-order computational complexity theory,…
An interesting family of geometric integrators for Lagrangian systems can be defined using discretizations of the Hamilton's principle of critical action. This family of geometric integrators is called variational integrators. In this…
We establish the Borg-Levinson theorem for elliptic operators of higher order with constant coefficients. The case of incomplete spectral data is also considered.
The paper considers a Clifford extension of the Grassmann algebra, in which operators are built from Grassmann variables and by the derivatives with respect to them. It is shown that a subalgebra which is isomorphic to the usual matrix…
We present a construction of a large class of Laplace invariants for linear hyperbolic partial differential operators of fairly general form and arbitrary order.
In this paper, we establish basic material for future investigations of the analysis and geometry of the twistor bundle, and of differential operators with the twistor bundle as source and/or target, especially the Rarita-Schwinger…
In this paper, we present a generalization of a Hamilton--Jacobi theory to higher order implicit differential equations. We propose two different backgrounds to deal with higher order implicit Lagrangian theories: the Ostrogradsky approach…
We functorially identify similarity classes of line-bundle-valued quadratic forms on rank two vector bundles with isomorphism classes of pairs consisting of the degree zero and the degree one parts of the associated generalized Clifford…
We construct the Heisenberg counterpart of a Clifford categorification. It is a modification of Khovanov's Heisenberg categorification. We express generators of the Heisenberg category as a complex of generators of the Clifford category.…
We study various kinds of Grassmannians or Lagrangian Grassmannians over $\mathbb{R}$, $\mathbb{C}$ or $\mathbb{H}$, all of which can be expressed as $\mathbb{G}/\mathbb{P}$ where $\mathbb{G}$ is a classical group and $\mathbb{P}$ is a…
In this paper we consider some Lie groups in complexified Clifford algebras. Using relations between operations of conjugation in Clifford algebras and matrix operations we prove isomorphisms between these groups and classical matrix groups…
Many difficulties of interpretation met by contemporary researchers attempting to recast or generalize Dirac's, Proca's, or Maxwell's theories using biquaternions or Clifford numbers have been encountered long ago by a number of physicists…
The aim of this paper is to study direct methods for the analyticity of the pressure for certain classical unbounded spin models. We provide a representation in terms of the Witten Laplacian on one-forms of the nth-derivative of the…
We classify the admissible types of constraint (hermitian, holomorphic, with reality conditions on the bosonic sectors, etc.) for generalized supersymmetries in the presence of complex spinors. We further point out which constrained…
We analyze the relation between the concept of auxiliary variables and the Inverse problem of the calculus of variations to construct a Lagrangian from a given set of equations of motion. The problem of the construction of a consistent…
For a second-order linear differential equation with two irregular singular points of rank three, multiple Laplace-type contour integral solutions are considered. An explicit formula in terms of the Stokes multipliers is derived for the…
We apply analytic bootstrap techniques to the four-point correlator of fundamental fields in the Wilson-Fisher model. In an $\epsilon$-expansion crossing symmetry fixes the double discontinuity of the correlator in terms of CFT data at…
We introduce the so-called Clifford-Gegenbauer polynomials in the framework of Dunkl operators, as well on the unit ball B(1), as on the Euclidean space $R^m$. In both cases we obtain several properties of these polynomials, such as a…
The covariantization procedure is usually referred to the translation operator, that is the derivative. Here we introduce a general method to covariantize arbitrary differential operators, such as the ones defining the fundamental group of…
First, we extend Leifer-Milner RPO theory, by giving general conditions to obtain IPO labelled transition systems (and bisimilarities) with a reduced set of transitions, and possibly finitely branching. Moreover, we study the weak variant…