Unitary representations of U/2,2/ and massless fields

Unitary representations of U-2,2 and massless field

Landau damping in a relativistic plasma

Landau damping in relativistic plasm

Sufficient conditions for curvature invariants to avoid divergencies in Hyperextended Scalar Tensor theory for Bianchi models

We look for sufficient conditions such that the scalar curvature, Ricci and Kretchmann scalars be bounded in Hyperextended Scalar Tensor theory for Bianchi models. We find classes of gravitation functions and Brans-Dicke coupling functions such that the theories thus defined avoid the singularity. We compare our results with these found by Rama in the framework of the Generalised Scalar Tensor theory for the FLRW models.Comment: 13 page

Mathematical surprises and Dirac's formalism in quantum mechanics

By a series of simple examples, we illustrate how the lack of mathematical concern can readily lead to surprising mathematical contradictions in wave mechanics. The basic mathematical notions allowing for a precise formulation of the theory are then summarized and it is shown how they lead to an elucidation and deeper understanding of the aforementioned problems. After stressing the equivalence between wave mechanics and the other formulations of quantum mechanics, i.e. matrix mechanics and Dirac's abstract Hilbert space formulation, we devote the second part of our paper to the latter approach: we discuss the problems and shortcomings of this formalism as well as those of the bra and ket notation introduced by Dirac in this context. In conclusion, we indicate how all of these problems can be solved or at least avoided.Comment: Largely extended and reorganized version, with new title and abstract and with 2 figures added (published version), 54 page