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A bosonic Laplacian, which is a generalization of Laplacian, is constructed as a second order conformally invariant differential operator acting on functions taking values in irreducible representations of the special orthogonal group,…
In this paper we consider successive iterations of the first-order differential operations in space ${\bf R}^3.$
We consider Hamiltonians, which are even polynomials of the forth order with the respect to Bose operators. We find subspaces, preserved by the action of Hamiltonian These subspaces, being finite-dimensional, include, nonetheless, states…
Given a self-adjoint operator $H\geq 0$ and (appropriate) densely defined and closed operators $P_{1},\dots, P_{n}$ in a Hilbert space $\mathscr{H}$, we provide a systematic study of bounded operators given by iterated integrals…
The evaluation of the higher twist contributions to Deep Inelastic Scattering amplitudes involves a non trivial choice of operator bases for the higher orders of the OPE expansion of the two hadronic currents. In this talk we discuss the…
By using the known operator product expansions (OPEs) between the lowest $16$ higher spin currents of spins $(1, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, 2,2,2,2,2,2, \frac{5}{2}, \frac{5}{2}, \frac{5}{2}, \frac{5}{2}, 3)$ in an…
We study gapped systems with anomalous time-reversal symmetry and global gravitational anomaly in three and four spacetime dimensions. These systems describe topological order on the boundary of bosonic Symmetry Protected Topological (SPT)…
This paper deals with the problem of factorizing integer powers of the Laplace operator acting on functions taking values in higher spin representations. This is a far-reaching generalization of the well-known fact that the square of the…
It is shown that the square of the Dirac Hamiltonian with the isotropic mass-hedgehog potential in d dimensions is the number operator of fictitious bosons and fermions over d quantum states. This result allows one to obtain the complete…
We provide the solution to the normal ordering problem for powers and exponentials of two classes of operators. The first one consists of boson strings and more generally homogeneous polynomials, while the second one treats operators linear…
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…
We rewrite the standard 4-dimensional Dirac equation in terms of quaternionic 2-component spinors, leading to a formalism which treats both massive and massless particles on an equal footing. The resulting unified description has the…
Proceeding from nonlinear realizations of (super)conformal symmetries, we explicitly demonstrate that adding the harmonic oscillator potential to the action of conformal mechanics does not break these symmetries but modifies the…
Odd-dimensional Riemannian spaces that are non-orientable, but have a pin structure, require the consideration of the twisted adjoint representation of the corresponding pin group. It is shown here how the Dirac operator should be modified,…
The type III Hermite $X_m$ exceptional orthogonal polynomial family is generalized to a double-indexed one $X_{m_1,m_2}$ (with $m_1$ even and $m_2$ odd such that $m_2 > m_1$) and the corresponding rational extensions of the harmonic…
Parafermions of order two and three are shown to be the fundamental tool to construct superspaces related to cubic and quartic extensions of the Poincar\'e algebra. The corresponding superfields are constructed, and some of their main…
We introduce new classes of right quaternionic Hilbert spaces of Bargmann-Fock type $\mathcal{GB}_{m}^{2}(\mathbb{H})$, labeled by nonnegative integer $m$, generalizing the so-called slice hyperholomorphic Bargmann-Fock space introduced…
We construct, in D=3,4,6 and 10 space-time dimensions, supersymmetric Lagrangians for free massless higher spin fields which belong to reducible representations of the Poincare group.The fermionic part of these models consists of…
We complete the construction of raising and lowering operators, given in a previous work, for the orthogonal polynomials of hypergeometric type on non-homogeneous lattice, and extend these operators to the generalized orthogonal…
We determine the spectrum of Kostant's cubic Dirac operator $D^{1/3}$ on locally symmetric Lorentzian manifolds of the form $\Gamma\backslash {\rm Osc}_1$, where ${\rm Osc}_1$ is the four-dimensional oscillator group and $\Gamma\subset {\rm…