We propose a generalization of the Bloch sphere representation for arbitrary spin states. It provides a compact and elegant representation of spin density matrices in terms of tensors that share the most important properties of Bloch vectors. Our representation, based on covariant matrices introduced by Weinberg in the context of quantum field theory, allows for a simple parametrization of cohe...

For two covariant differential ∗-calculi, the twisted cyclic cocycle associated with the volume form is represented in terms of commutators [F , ρ(x)] for some self-adjoint operator F and some ∗-representation ρ of the underlying ∗-algebra. MSC (2000): 17B37; 46L87; 81R50

We show the light-front representation of the field theoretical Bethe-Salpeter equation (BSE) in the ladder approximation using the quasi potential reduction. We discuss the equivalence of the covariant ladder Bethe-Salpeter equation with an infinite set of coupled equations for the Green’s functions of the different light-front Fock-states.

In this paper, we construct a single Lagrangian for both limits of Galilean electrodynamics. The framework relies on covariant formalism used in describing Newton-Cartan geometry. We write down the conformal algebra and its representation formalism. also show that is invariant under d = 4 calculate energy-momentum tensor.

We focus on the irreducibility of wavelet representations. We present some connections between the following notions: covariant wavelet representations, ergodic shifts on solenoids, fixed points of transfer (Ruelle) operators and solutions of refinement equations. We investigate the irreducibility of the wavelet representations, in particular the representation associated to the Cantor set, int...

The quantum general linear supergroup GL q (m|n) is defined and its structure is studied systematically. Quantum homogeneous supervector bundles are introduced following Connes' theory, and applied to develop the representation theory of GL q (m|n). Quantum Frobenius reciprocity is proven, and a Borel-Weil theorem is established for the covariant and contravariant tensor irreps.

A notion of Cartan pairs as an analogy of vector fields in the realm of noncommutative geometry has been proposed in [2]. In this paper we give an outline of the construction of a noncommutative analogy of the algebra of partial differential operators as well as its natural (Fock type) representation. We shall also define co-universal vector fields and covariant derivatives.

1. In the mathematical theory of fields of elementary particles one has to do with a representation of the unitary group on a Hilbert space 77. With any such representation T and subspace M of 77 there is associated a self-adjoint operator called the "number of particles in M." The particle interpretation of general wave fields is made possible in the first instance by the fact that these opera...

We study in detail the irreducible representation of [Formula: see text] theory that corresponds to massless particles. This has little algebra and contains 128 physical states belong spinor text]. These are degrees freedom maximal supergravity eleven dimensions. smaller number freedom, compared what might be expected, is due an infinite duality relations which turn can traced existence a subag...

Spinor representation of the group GL(4,R) is needed for correct description of the Fermi fields on Riemann space, such as the space-time of general relativity. It is used for two purposes: to define the connectivity and covariant derivative of spinor field and to define the Lie derivative. Recent publications [1–3] have reminded of this problem. The important problem for definition of Fermi fi...