Centre de Physique Théorique


Wednesday 16 January 2019

11h00 – 12h00, CPT, Amphi 5

Semiclassical dynamics on singular spaces. Relation to the properties of geodesic flows and to certain problems of analytic number theory

Andrei Shafevich (Moscou)


We study propagation of quasi-particles (localized semi-classical solutions of the Schroedinger equation) on singular spaces. Such spaces can be obtained from metric graphs via replacing vertices by smooth Riemannian manifolds. We describe both local and global behaviour of quasi-particles. Local behaviour is governed by Maslov canonical operator modified near the points of gluing. The global large-time statistics is related to the properties of geodesics as well as to certain problems of Analytic Number Theory (the problem of distribution of abstract primes and the problem of counting the lattice points in growing polyhedra).

14h00 – 15h00, CPT, Amphi 5

Kaluza-Klein and Nelson mechanisms reinterpreted on extended phase-space for reconciling General Relativity with Quantum Mechanics

Claudio Di Troia (ENEA, FSN dipartment)


Kaluza-Klein mechanism was rejected for inconsistencies due to the
Planck length scale.
Nelson derivation of Quantum Mechanics was rejected for having assumed,
without justification, a multivalued action and the presence of
universal fluctuations. Both the mechanisms can be reinterpreted without
problems at the light of the guiding center (for Kaluza-Klein) and
gyrocenter (for Nelson) transformations. It is demonstrated that with
the use of guiding center coordinates the fields follow an Einstein’s
equation on the phase-space extended to time and Gravitation includes
electromagnetism if considered on such extended phase space. Once
electromagnetic (now also gravitational) fluctuations are considered it
is shown that the gyrocenter follows the Schroedinger equation. It is
proposed to explaining the discrepancies between GR and QM in the
simplest way: they are describing different objects (guiding center and
gyrocenter, respectively) that are both representative of charges and/or
masses. In this way a unified theory is accessible and it can be
depicted without inconsistencies.