Electromagnetic mass shifts, equal-time commutators (ETC), and their relation are analyzed, using the Jost-Lehmann representation for the forvrard Compton amplitude, The divergences in 6m are determined by Lorentz scal@rs associated with the ETC (when these exist). These results are illustrated by models with currents bilinear and linear in canonical fields. Existence of the ETC implies that th...

We study the group of interval exchange transformations and obtain several characterizations of its commutator group. In particular, it turns out that the commutator group is generated by elements of order 2.

For the q-deformation Gq , 0 < q < 1, of any simply connected simple compact Lie group G we construct an equivariant spectral triple which is an isospectral deformation of that defined by the Dirac operator D on G. Our quantum Dirac operator Dq is a unitary twist of D considered as an element of Ug ⊗ Cl(g). The commutator of Dq with a regular function on Gq consists of two parts. One is a twist...

In a general algebraic setting, we state some properties of commutators of reflexive admissible relations. After commutator theory in Universal Algebra has been discovered about thirty years ago [12], many important results and applications have been found. An introduction to commutator theory for congruence modular varieties can be found in [2] and [3]. Shortly after, results valid for larger ...

The aim of this paper is to establish the vector-valued inequalities for Littlewood-Paley operators, including the Lusin area integrals, the Littlewood-Paley g-functions and g∗μ-functions, and their commutators on the Herz-Morrey spaces with variable exponentMK̇ p,q(·)(R n). By applying the properties of Lp(·)(Rn) spaces and the vector-valued inequalities for Littlewood-Paley operators and their...