Related papers: Second order symmetry operators
We compute conformal correlation functions with spinor, tensor, and spinor-tensor primary fields in general dimensions with Euclidean and Lorentzian metrics. The spinors are taken to be Dirac spinors, which exist for any dimensions. For…
On the basis of the Wigner unitary representations of the covering group ISL(2,C) of the Poincar\'{e} group, we obtain spin-tensor wave functions of free massive particles with arbitrary spin. The wave functions automatically satisfy the…
We study the Lie point symmetries of a general class of partial differential equations (PDE) of second order. An equation from this class naturally defines a second-order symmetric tensor (metric). In the case the PDE is linear on the first…
This paper studies formulations of second-order elliptic partial differential equations in nondivergence form on convex domains as equivalent variational problems. The first formulation is that of Smears \& S\"uli [SIAM J.\ Numer.\ Anal.\…
The Rarita-Schwinger-Seiberg-Witten (RS-SW) equations are defined similarly to the classical Seiberg-Witten equations, where a geometric non-Dirac-type operator replaces the Dirac operator called the Rarita-Schwinger operator. In dimension…
We give a classification of $1^{st}$ order invariant differential operators acting between sections of certain bundles associated to Cartan geometries of the so called metaplectic contact projective type. These bundles are associated via…
We look at smooth manifolds equipped with a possibly singular Riemannian metric. We give sufficient conditions for the existence of scalar curvature measures and Dirac operators.
This is the second part of an article about q-deformed analogs of spinor calculus. The considerations refer to quantum spaces of physical interest, i.e. q-deformed Euclidean space in three or four dimensions as well as q-deformed Minkowski…
We introduce new aspects in conformal geometry of some very natural second-order differential operators. These operators are termed shift operators. In the flat space, they are intertwining operators which are closely related to symmetry…
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…
Olver and Rosenau studied group-invariant solutions of (generally nonlinear) partial differential equations through the imposition of a side condition. We apply a similar idea to the special case of finite-dimensional Hamiltonian systems,…
We show how conformal partial waves (or conformal blocks) of spinor/tensor correlators can be related to each other by means of differential operators in four dimensional conformal field theories. We explicitly construct such differential…
A computer-algebra aided method is carried out, for determining geometric objects associated to differential operators that satisfy the elliptic ansatz. This results in examples of Lame curves with double reduction and in the explicit…
We develop a classification of composite operators without gradients at Anderson-transition critical points in disordered systems. These operators represent correlation functions of the local density of states (or of wave-function…
By solving the two variable differential equations which arise from finding the eigenfunctions for the Casimir operator for $O(d,2)$ succinct expressions are found for the functions, conformal partial waves, representing the contribution of…
The second-order differential equation describes harmonic oscillators, as well as currents in LCR circuits. This allows us to study oscillator systems by constructing electronic circuits. Likewise, one set of closed commutation relations…
Motivated by applications in computational anatomy, we consider a second-order problem in the calculus of variations on object manifolds that are acted upon by Lie groups of smooth invertible transformations. This problem leads to solution…
Modifications of Dirac operators in supergravity flux backgrounds are considered. Modified spin curvature operators and squares of modified Dirac operators corresponding to Schr\"odinger-Lichnerowicz-like formulas are obtained for different…
Lie's linearizability criteria for scalar second-order ordinary differential equations had been extended to systems of second-order ordinary differential equations by using geometric methods. These methods not only yield the linearizing…
We analyze dispersion relations of the equations recently proposed by Ahluwalia for describing neutrino. Equations for type-II spinors are deduced on the basis of the Wigner rules for left- and right- 2-spinors and the Ryder-Burgard…