Descripción: Applying the doublet representation we analyze the solutions of a Hamiltonian system which has eigenstates with complex eigenvalues. The example of the Friedrichs model allows us to show how the appearance of solutions with non-Hilbert initial conditions is linked to the energy degeneration of the Hamiltonian spectrum. We discuss the difficulties of giving a physical meaning to the growing or decaying non-Hilbert solutions. We also suggest a way to circumvent the problem of the anomalous probabilities related to both complex energy eigenvalues and degeneration of the spectrum. © 1998 American Institute of Physics.

Descripción: The complete set of concomitants is given of the metric, a scalar function, and their derivatives in six dimensions without imposing conditions on the order of the derivatives and their properties are studied under conformal transformations. These results are useful in several physical problems, like finding φ2ren and Τμν ren in any geometry. © 1992 American Institute of Physics.

Descripción: Weyl's theorem is extended making use of the theory of concomitants to obtain a Lagrangian density for the massless bosonic fields without dimensional constants. It turns out to be quadratic in the gravitational field and encompasses all the theories that usually appear in the literature. It is shown that the gauge invariance of the Lagrangian follows from the invariance of the field equations. © 1987 American Institute of Physics.