In front-form dynamics the current operator can be constructed from auxiliary operators, defined in a Breit frame where initial and final three-momenta of the system are directed along the z axis. Poincaré covariance constraints reduce for auxiliary operators to the ones imposed only by kinematical rotations around the z axis. Elastic and transition form factors can be extracted without any amb...

we present a general theory of $ilii~ear/ quadratic signal representations t h a t a l e coiianant to timefrequency (TF) displacement operators resentations are developed in the CY,,^') dQmaiiB and iio the e e o ~ ~ u ~ a ~ e case, covariant representa,tions can also be formulated in an eigenfunction parameter domain ( ( a , b ) domain). The relations connecting the (0, p), TF, and (U, b) domai...

The well known conformal covariance of the Dirac operator acting on spinor fields does not extend to its powers in general. For odd powers of the Dirac operator we derive an algorithmic construction in terms of associated tractor bundles computing correction terms in order to achieve conformal covariance. These operators turn out to be formally (anti-) self-adjoint. Working out this algorithm w...

Some new identities for quantum variance and covariance involving commutators are presented, in which the density matrix and the operators are treated symmetrically. A measure of entanglement is proposed for bipartite systems, based upon covariance. This works for two-and three-component systems but produces ambiguities for multicomponent systems of composite diemnsion. Its relationship to angu...

The expanding role of positional covariance data in modern spacecraft operations leads to a need for better understanding of the time evolution of covariance by mission planners and operators. It is common to see positional covariance information presented as uncertainties in the radial, cross-track and in-track directions. While such a time history does provide some information, it tends to ob...

This paper introduces a novel mathematical and computational framework, namely Log-Hilbert-Schmidt metric between positive definite operators on a Hilbert space. This is a generalization of the Log-Euclidean metric on the Riemannian manifold of positive definite matrices to the infinite-dimensional setting. The general framework is applied in particular to compute distances between covariance o...

Optimum filters for an image restoration are formed by a degradation operator, a covariance operator of original images, and one of noise. However, in a practical image restoration problem, the degradation operator and the covariance operators are estimated on the basis of empirical knowledge. Thus, it appears that they differ from the true ones. When we restore a degraded image by an optimum f...