Related papers: A weighted de Rham operator acting on arbitrary te…
We investigate the complex of differential forms in curved, six-dimensional, $N=(1,0)$ superspace. The superconformal group acts on this complex by super-Weyl transformations. An ambi-twistor-like representation of a second conformal group…
We demonstrate that the two (1 + 1)-dimensional (2D) free 1-form Abelian gauge theory provides an interesting field theoretical model for the Hodge theory. The physical symmetries of the theory correspond to all the basic mathematical…
We prove a theorem on scalar-valued functions of tensors, where ``scalar'' refers to absolute scalars as well as relative scalars of weight $w$. The present work thereby generalizes an identity referred to earlier by Rosenfeld in his…
By the Moutard transformation method we construct two-dimensional Schrodinger operators with real smooth potential decaying at infinity and with a multiple positive eigenvalue. These potentials are rational functions of spatial variables…
Let $M$ be an $n$-dimensional manifold, $V$ the space of a representation $\rho: GL(n)\longrightarrow GL(V)$. Locally, let $T(V)$ be the space of sections of the tensor bundle with fiber $V$ over a sufficiently small open set $U\subset M$,…
In this paper, we prove analogues of O'Neil's inequalities for the convolution in the weighted Lebesgue spaces. We also establish the weighted two-sided norm inequalities for the potential operator.
We consider odd Laplace operators acting on densities of various weight on an odd Poisson (= Schouten) manifold $M$. We prove that the case of densities of weight 1/2 (half-densities) is distinguished by the existence of a unique odd…
We decompose the de Rham Laplacian on Sasaki-Einstein manifolds as a sum over mostly positive definite terms. An immediate consequence are lower bounds on its spectrum. These bounds constitute a supergravity equivalent of the unitarity…
We show how, using different decompositions of E(11), one can calculate the representations under the duality group of the so--called "de-form" potentials. Evidence is presented that these potentials are in one-to-one correspondence to the…
Centered weighted composition operators on $L^2$-spaces are characterized. The characterization is obtained without the assumption that the operator is a product of a multiplication and a composition operator. The concept of spectrally…
In this paper the W-algebra W(2,2) and its representation theory are studied. It is proved that a simple vertex operator algebra generated by two weight 2 vectors is either a vertex operator algebra associated to a highest irreducible…
In the last few years renewed interest in the 3-tensor potential $L_{abc} $ proposed by Lanczos for the Weyl curvature tensor has not only clarified and corrected Lanczos's original work, but generalised the concept in a number of ways. In…
We study the effective potential for composite operators. Introducing a source coupled to the composite operator, we define the effective potential by a Legendre transformation. We find that in three or fewer dimensions, one can use the…
Locally variational systems of differential equations on smooth manifolds, having certain de Rham cohomology group trivial, automatically possess a global Lagrangian. This important result due to Takens is, how-ever, of sheaf-theoretic…
We discuss the generalisation of the Weyl double copy to higher spin "multi-copies", showing how the natural linearised higher spin field strengths can be related to sums of powers of the Maxwell tensor. The tracelessness of the field…
General formulas of the two-electron operator representing either atomic or effective interactions are given in a coupled tensorial form in relativistic approximation. The alternatives of using uncoupled, coupled and antisymmetric…
We consider a generalization of the Riesz operator in $R^d$ and obtain estimates for its norm and for related capacities via the modified Wolff potential. These estimates are based on the certain version of $T1$ theorem for…
Starting from a manifestly Lorentz- and diffeomorphism-invariant classical action we perform a perturbative derivation of the gravitational anomalies for chiral bosons in 4n+2 dimensions. The manifest classical invariance is achieved using…
Suppose that $\Omega$ is the open region in $\mathbb{R}^n$ above a Lipschitz graph and let $d$ denote the exterior derivative on $\mathbb{R}^n$. We construct a convolution operator $T $ which preserves support in $\bar{\Omega$}, is…
We study the tomography of multispin quantum states in the context of finite-dimensional Wigner representations. An arbitrary operator can be completely characterized and visualized using multiple shapes assembled from linear combinations…