A concrete procedure for obtaining sharp reconstructions of unsharp observables in finite-dimensional quantum mechanics

We discuss the problem of how a (commutative) generalized observable in a finite-dimensional Hilbert space (communtative effect-valued resolution of the identity) can be considered as an unsharp realization of some standard observable (projection-valued resolution of the identity). In particular, we give a concrete procedure for constructing such a standard observable. Some results about the “uniqueness” of the resulting observable are also examined.     

System linearization via feedback: A control engineering perspective

The possibility of using feedback to achieve or to enhance system linearity is well known to control engineers since decades ago. A few major breakthroughs, made possible by the application of differential geometric tools to control theoretic issues, have revamped a new interest in all facets of the problem, including the search, the analysis and the computation of suitable approximate solutions. In the present paper, recent developments and new trends in the field are shortly reviewed, with special attention paid to some research issues currently addressed by the authors. Though primarily meant for learned mathematically oriented readers, the presentation focuses on ideas and concepts more than on their most general and mathematically rigorous formulations. On the other hand, it does not assume familiarity with advanced control theory nor modern control technology.     

Six-fermion calculation of intermediate-mass Higgs boson production at future {e^+ e^-} colliders

The production of an intermediate-mass Higgs boson in processes of the kind fermions at the energies of future linear colliders is studied. The recently developed and fully automatic algorithm/code ALPHA is used to compute the tree-level scattering amplitudes for the reactions . The code has been interfaced with the Monte Carlo program HIGGSPV/WWGENPV, properly adapted to 6-fermion production, in order to provide realistic results, both in the form of cross sections and event samples at the partonic level. Phenomenological results, that incorporate the effects of initial-state radiation and beamstrahlung, are shown and commented, emphasizing the potentials of full six-fermion calculations for precise background evaluation as well as for detailed studies of the fundamental properties of the Higgs particle. Received: 22 May 1997 / Published online: 20 February 1998     

Can the Local Energy-Momentum Conservation Laws be Derived Solely from Field Equations?

The vanishing of the divergence of the matter stress-energy tensor for General Relativity is a particular case of a general identity, which follows from the covariance of the matter Lagrangian in much the same way as (generalized) Bianchi identities follow from the covariance of the purely gravitational Lagrangian. This identity, holding for any covariant theory of gravitating matter, relates the divergence of the stress tensor with a combination of the field equations and their derivatives. One could thus wonder if, according to a recent suggestion [1], the energy-momentum tensor for gravitating fields can be computed through a suitable rearrangement of the matter field equations, without relying on the variational definition. We show that this can be done only in particular cases, while in general it leads to ambiguities and possibly to wrong results. Moreover, in nontrivial cases the computations turn out to be more difficult than the standard variational technique.     

On a theorem by do Carmo and Dajczer

We give a new proof of a theorem by M.P. do Carmo and M. Dajczer on helicoidal surfaces of constant mean curvature.