Canonical transformations for relativistic particles

A class of relatively simple canonical transformations of the Dirac equation, which contains as a particular case the Foldy-Wouthuysen transformation, is determined. An exact form for the hamiltonian of a Dirac-Pauli electron is obtained.     

Zeta Function on a Generalised Cone

The analytic properties of the -function for a Laplace operator on a generalised cone are studied in some detail using Cheeger's approach and explicit expressions are given. In the compact case, the -function of the Laplace operator turns out to be singular at the origin. As a result, strictly speaking, the -function regularisation does not regularise and a further subtraction is required for the related one-loop effective potential.     

On the Stability of a Class of Modified Gravitational Models

Motivated by the dark energy issue, a minisuperspace approach to the stability for modified gravitational models in a four dimensional cosmological setting is investigated. Specifically, after revisiting the f(R) case, R being the Ricci curvature, we present a stability condition around a de Sitter solution valid for modified gravitational models of generalized type F(R,G,Q), G and Q being the Gauss-Bonnet and quadratic Riemann invariants respectively. A generalization to higher order invariants is presented.     

Consistent,Covariant and Multiplicative Anomalies

It is shown that the multiplicative anomaly in the vector-axial-vector model, which apparently has nothing to do with the breaking of classical current symmetries, nevertheless is strictly related to the well known consistent and covariant anomalies.     

Homogeneous Cosmologies in Generalized Modified Gravity

Dynamical system methods are used in the study of the stability of spatially flat homogeneous cosmologies within a large class of generalized modified gravity models in the presence of a relativistic matter-radiation fluid. The present approach can be considered as the generalization of previous works in which only F(R) cases were considered. Models described by an arbitrary function of all possible geometric invariants are investigated and general equations giving all critical points are derived.     

Gravitational theories with de Sitter constant vacuum solution

We consider a large class of geometric Lagrangian forms defined in the manifold of the reference frames. The theories described by those Lagrangians are such that, in an empty region, the manifold can be identified with one of the de Sitter groups. The Lagrangian forms are classified according to their symmetry properties with respect to transformation groups acting on the linear space of the infinitesimal transformations of the frames. Requiring invariance with respect to aSO(3) group and a reasonable physical behavior under space reflections, we obtain only three different theories. Then we show that every Lagrangian form of the kind we are considering, is equivalent to anSO(3)-invariant one.     

Relativistic wave mechanics of spinless particles in a curved space-time

Starting from the Klein-Gordon equation, the single-particle approximation for a reiativistic scalar particle in the presence of external electromagnetic and gravitational fields is performed. The nonrelativistic limit is obtained by a Foldy-Wouthuysen transformation on a Schrödinger-type equation. The results are then compared with those obtained in classical mechanics.