Related papers: On quantum numbers for Rarita-Schwinger fields
In this paper we derive the most general first-order symmetry operator commuting with the Dirac operator in all dimensions and signatures. Such an operator splits into Clifford even and Clifford odd parts which are given in terms of odd…
We determine the general form of the first order linear symmetry operators for the linearized field equation of metric perturbations in the spacetimes of dimension D>=4. Apart from the part derived easily from the invariance under general…
The problem of d-dimensional Schrodinger equations with a position-dependent mass is analyzed in the framework of first-order intertwining operators. With the pair (H, H_1) of intertwined Hamiltonians one can associate another pair of…
We study the ladder operator on scalar fields, mapping a solution of the Klein-Gordon equation onto another solution with a different mass, when the operator is at most first order in derivatives. Imposing the commutation relation between…
We consider first order symmetry operators for the equations of motion of differential $p$-form fields in general $D$-dimensional background geometry of any signature for both massless and massive cases. For $p=1$ and $p=2$ we give the…
The second order symmetry operators that commute with the Dirac operator with external vector, scalar and pseudo-scalar potentials are computed on a general two-dimensional spin-manifold. It is shown that the operator is defined in terms of…
It has been shown that, for all dimensions and signatures, the most general first-order linear symmetry operators for the Dirac equation including interaction with Maxwell field in curved background are given in terms of Killing-Yano (KY)…
This article explores an algebraic-recursive approach to construct differential operators that commute with a central operator $\hat{H}$ in quantum mechanics. Starting from the Schr\"odinger equation for a free particle, the work derives…
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 study a generalization of the classical Rarita-Schwinger type operators and construct their fundamental solutions. We give some basic integral formulas related to these operators. We also establish that the projection…
It has been revealed that the first order symmetry operator for the linearized Einstein equation on a vacuum spacetime can be constructed from a Killing-Yano 3-form. This might be used to construct all or part of solutions to the field…
In this paper we discuss some results related to commuting ordinary differential operators of rank greater than one.
There is a certain family of conformally invariant first order elliptic operators on Riemannian spin manifold which include Dirac operator as its first and simplest member. Their general definition is given and their basic properties are…
In this paper we study some operators associated to the Rarita-Schwinger operators. They arise from the difference between the Dirac operator and the Rarita-Schwinger operators. These operators are called remaining operators. They are based…
We consider the Klein-Gordon equation in generalized higher-dimensional Kerr-NUT-(A)dS spacetime without imposing any restrictions on the functional parameters characterizing the metric. We establish commutativity of the second-order…
We consider one-point commuting difference operators of rank one. The coefficients of these operators depend on a functional parameter, shift operators being included only with positive degrees. We study these operators in the case of…
We show that the first-order symmetry operators of twistor spinors can be constructed from conformal Killing-Yano forms in conformally-flat backgrounds. We express the conditions on conformal Killing-Yano forms to obtain mutually commuting…
It is shown that the Dirac equation is separable by variables in a five-dimensional rotating Kerr-(anti-)de Sitter black hole with two independent angular momenta. A first order symmetry operator that commutes with the Dirac operator is…
Several algebro-geometric properties of commutative rings of partial differential operators as well as several geometric constructions are investigated. In particular, we show how to associate a geometric data by a commutative ring of…
We construct the algebra of operators acting on the Hilbert spaces of Quantum Mechanics for systems of $N$ identical particles from the field operators acting in the Fock space of Quantum Field Theory by providing the explicit relation…