We consider the conformal properties of geometries described by higher-rank line elements. A crucial role is played by the conformal Killing equation (CKE). We introduce the concept of null-flat spaces in which the line element can be written as ds = r!dζ1 · · ·dζr. We then show that, for null-flat spaces, the critical dimension, for which the CKE has infinitely many solutions, is equal to the ...

In the modern theory of quantum mechanics, observables are represented as normalized positive operator valued measures (POVMs). The set of all POVMs having the same outcome space has natural convex structure. A convex mixture of two POVMs corresponds to a random choice between two measurement apparatuses. An extremal POVM thus describes an observable which is unaffected by this kind of randomne...

In this note we discuss some symmetry groups as nice examples of group extensions. We begin by a short general discussion of symmetry groups. An isometry of R is a distancepreserving bijection of R. For examples of isometries, translations by a vector, rotations about a point, and reflections about a hyperplane are all isometries. Let Isom(R) be the set of all isometries of R. This is a group u...

A snake-in-the-box code (or snake) of word length n is a simple circuit in an n-dimensional cube Qn , with the additional property that any two non-neighboring words in the circuit differ in at least two positions. To construct such snakes a straightforward, non-recursive method is developed based on special linear codes with minimum distance 4. An extension of this method is used for the const...

Using a linear mass spectrum of an SU(4) meson hexadecuplet, we derive the Gell-Mann–Okubo mass formula for the charmed mesons, in good agreement with experiment. Possible generalization of this method to a higher symmetry group is briefly discussed. Bitnet: [email protected] Bitnet: [email protected]. On sabbatical leave from School of Physics and Astronomy, Tel Aviv University, Ramat Avi...

The symmetry rule in propositional logic allows the exploitation of symmetries present in a problem. In the context of resolution, the rule enables the shortening of refutations by using symmetries present in an initial set of clauses. These symmetries can be local or global. The present paper proves that the local symmetry rule is strictly more powerful than the global symmetry rule. It also e...

When a material which is isotropic with respect to a reference configuration is deformed, it is anisotropic with respect to the deformed configuration. The nature of the anisotropy depends on the deformation. In this paper, we consider the special case of the change of a reference configuration by uniaxial extension. We first discuss the structure of the new material symmetry group, and show th...

We discuss the relation between space–time diffeomorphisms and gauge transformations in theories of the Yang–Mills type coupled with Einstein’s general relativity. We show that local symmetries of the Hamiltonian and Lagrangian formalisms of these generally covariant gauge systems are equivalent when gauge transformations are required to induce transformations which are projectable under the Le...

We study a charged particle in an electromagnetic field without kinetic or potential term. Although dynamically trivial, this system is interesting because it has an infinite dimensional symmetry group. We discuss the way in which this group behaves under quantization. Ref. SISSA XX/91/EP (February 1991)

Ray tracing in spherical Luneburg lenses has always been represented in 2D. All propagation planes in a 3D spherical Luneburg lens generate the same ray tracing, due to its radial symmetry. A geometry without radial symmetry generates a different ray tracing. For this reason, a new ray tracing method in 3D through spherical and elliptical Luneburg lenses using 2D methods is proposed. The physic...