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Higher order higher spin operators are generalizations of $kth$-powers of the Dirac operator. In this paper, we study higher order higher spin operators defined on some conformally flat manifolds, namely cylinders and Hopf manifolds. We…
This paper studies a particular class of higher order conformally invariant dif- ferential operators and related integral operators acting on functions taking values in particular finite dimensional irreducible representations of the Spin…
In this paper, we establish higher order Borel-Pompeiu formulas for conformally invariant fermionic operators in higher spin theory, which is the theory of functions on m-dimensional Euclidean space taking values in arbitrary irreducible…
We present a construction of fermionic operators in 3+1 dimensions in terms of bosonic fields in the framework of $QED_4$. The basic bosonic variables are the electric fields $E_i$ and their conjugate momenta $A_i$. Our construction…
We construct Schroedinger-like solutions of the Vasiliev higher spin theory in D>3 dimension. Symmetries of such solutions and the linearised equation of motion for the scalar on such backgrounds are analysed. We further propose Galilean…
We introduce prepotentials for fermionic higher-spin gauge fields in four spacetime dimensions, generalizing earlier work on bosonic fields. To that end, we first develop tools for handling conformal fermionic higher-spin gauge fields in…
This paper completes the construction of arbitrary order conformally invariant differential operators in higher spin spaces. Jan Slov\'{a}k has classified all conformally invariant differential operators on locally conformally flat…
In this article, we explicitly compute in momentum space the three and four-point correlation functions involving scalar and spinning operators in the free bosonic and the free fermionic theory in three dimensions. We also evaluate the…
We pursue the idea of constructing higher spin fields as solutions to twisted Dirac operators. As general results we find that twisted prenormally hyperbolic first order operators (such as the Dirac operator) on globally hyperbolic…
The Dirac operator for a manifold Q, and its chirality operator when Q is even dimensional, have a central role in noncommutative geometry. We systematically develop the theory of this operator when Q=G/H, where G and H are compact…
We study the higher spin Dirac operators on 3-dimensional manifolds and show that there exist two Laplace type operators for each associated bundle. Furthermore, we give lower bound estimations for the first eigenvalues of these Laplace…
This paper deals with a certain class of second-order conformally invariant operators acting on functions taking values in particular (finite-dimensional) irreducible representations of the orthogonal group. These operators can be seen as a…
We discuss an extension of higher order topological phases to include bosonic systems. We present two spin models for a second-order topological phase protected by a global $\mathbb{Z}_2\times\mathbb{Z}_2$ symmetry. One model is built from…
Quaternionic and octonionic spinors are introduced and their fundamental properties (such as the space-times supporting them) are reviewed. The conditions for the existence of their associated Dirac equations are analyzed. Quaternionic and…
This paper is dedicated to the construction of multidimensional spherical monogenics. Firstly, we investigate the construction of monogenic functions in dimension $3$ by applying the Dirac operator to the orthonormal bases of spherical…
We present a generalization of the Clifford action for other representations spaces of $Spin(n)$, which is called the Clifford homomorphism. Their properties extend to the ones for the higher spin Dirac operators on spin manifolds. In…
As it has been proven, the determination of general one-dimensional Schr\"odinger Hamiltonians having third-order differential ladder operators requires to solve the Painlev\'e IV equation. In this work, it will be shown that some specific…
We emphasize some properties of coherent state groups, i.e. groups whose quotient with the stationary groups, are manifolds which admit a holomorphic embedding in a projective Hilbert space. We determine the differential action of the…
In this article, we firstly introduce higher spin Clifford analysis, which are considered as generalizations of classical Clifford analysis by considering functions taking values in irreducible representations of the spin group. Then, we…
Recent works have sought to realize certain families of orthogonal, symmetric polynomials as partition functions of well-chosen classes of solvable lattice models. Many of these use Boltzmann weights arising from the trigonometric…