Prof. Gary Gibbons
In residence at
Prof. Sergey Solodukhin
Classical and Quantum Space-Time and Its Symmetries
There is accumulating evidence that in the next decades gravitational physics shall play an important and dominating role in expanding, both theoretically and experimentally, the existing horizons of our knowledge of fundamental laws of Nature. In this project it is proposed to study theoretically both the classical and quantum properties of space-time and its symmetries, focusing efforts in this extremely promising direction of contemporary research.
The project is based on the strong scientific ties and on-going collaboration between members of IDP. The main objective is to use the proposed program of collaboration as a centre of crystallization for otherwise diverse scientific interests of different members of the laboratory in general, and of the theoretical Gravity and Field Groups in particular.
Publications in relation with the research project
The Eisenhart lift of a Paul trap used to store ions in molecular physics is a linearly polarized periodic gravitational wave. A modified version of Dehmelt’s Penning trap is, in turn, related to circularly polarized periodic gravitational waves, sought in inflationary models. Similar equations also govern the Lagrange points in celestial mechanics. The explanation is provided by anisotropic oscillators.
Kepler's rescaling becomes, when “Eisenhart-Duval lifted” to 5-dimensional “Bargmann” gravitational wave spacetime, an ordinary spacetime symmetry for motion along null geodesics, which are the lifts of Keplerian trajectories. The lifted rescaling generates a well-behaved conserved Noether charge upstairs, which takes an unconventional form when expressed in conventional terms. This conserved quantity seems to have escaped attention so far. Applications include the Virial Theorem and also Kepler's Third Law. The lifted Kepler rescaling is a Chrono-Projective transformation. The results extend to celestial mechanics and Newtonian Cosmology.