Related papers: Bosonic Laplacians in higher spin Clifford analysi…
We present a new representation of spin operators in terms of bosonic creation-annihilation operators. This representation allows us to formulate a new field-theoretical description of spin systems which is free of any constraints. The…
Recently a new technique in the harmonic analysis on symmetric spaces was suggested based on certain remarkable representations of affine and double affine Hecke algebras in terms of Dunkl and Demazure operators instead of Lie groups and…
Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged and nonexpansive operators. The structure and properties of the compositions are of…
We discuss an elementary derivation of variational symmetries and corresponding integrals of motion for the Lagrangian systems depending on acceleration. Providing several examples, we make the manuscript accessible to a wide range of…
We first strictly expressed the basic notions and research methods of abstract operators, which systematically expounded the main results of abstract operator theory. By combining abstract operators with the Laplace transform, we can easily…
A Clifford algebra over the binary field 2 = {0,1} is a second-order classical logic that is substantially richer than Boolean algebra. We use it as a bridge to a Clifford algebraic quantum logic that is richer than the usual Hilbert space…
In this largely expository paper we give a self-contained treatment of the Dirac operator. Emphasizing the algebraic point of view we first sketch the necessary prerequisites from Clifford algebras and their representations and then define…
A representation of the quadratic Dirac equation and the Maxwell equations in terms of the three-dimensional universal complex Clifford algebra is given. The investigation considers a subset of the full algebra, which is isomorphic to the…
A new relativistic description of quantum electrodynamics is presented. Guideline of the theory is the Klein-Gordon equation, which is reformulated to consider spin effects. This is achieved by a representation of relativistic vectors with…
Here we define Rarita-Schwinger operators on cylinders and construct their fundamental solutions. Further the fundamental solutions to the cylindrical Rarita-Schwinger type operators are achieved by applying translation groups. In turn, a…
In this article, we give all the Weitzenb\"ock-type formulas among the geometric first order differential operators on the spinor fields with spin $j+1/2$ over Riemannian spin manifolds of constant curvature. Then we find an explicit…
Higher-spin diffeomorphisms are to higher-order differential operators what diffeomorphisms are to vector fields. Their rigorous definition is a challenging mathematical problem which might predate a better understanding of higher-spin…
In this paper we adapt the technique developed in [17] to show that many harmonic analysis operators in the Bessel setting, including maximal operators, Littlewood-Paley-Stein type square functions, multipliers of Laplace or…
Worldline quantum field theory (WQFT) has proven itself a powerful tool for classical two-body scattering calculations in general relativity. In this paper we develop a new worldline action involving bosonic oscillators, which enables the…
In this paper we solve the problem on finding a sectionally Clifford algebra-valued harmonic function, zero at infinity and satisfying certain boundary value condition related to higher order Lipschitz functions. Our main tool are the Hardy…
We study invariant operators in general tensor models. We show that representation theory provides an efficient framework to count and classify invariants in tensor models. In continuation and completion of our earlier work, we present two…
A universal description of particles with spins j greater or equal one , transforming in (j,0)+(0,j), is developed by means of representation specific second order differential wave equations without auxiliary conditions and in covariant…
We study Laplacians on general countable weighted simplicial complexes from a conceptual point of view. These operators will first be introduced formally before showing that those formal operators coincide with self-adjoint realizations of…
An explicit algorithmic construction is given for orthogonal bases for spaces of homogeneous polynomials, in the context of Hermitean Clifford analysis, which is a higher dimensional function theory centred around the simultaneous null…
The known equivalence of 8-dimensional chiral spinors and vectors, also referred to as triality, is discussed for (4+4)-space. Split octonionic representation of SO(4,4) and Spin(4,4) groups and the trilinear invariant form are explicitly…