As an extension of Gabor signal processing, the covariant Weyl-Heisenberg integral quantization is implemented to transform  functions on the eight-dimensional  phase space (x,k) into Hilbertian operators. The x=(x^{\mu}) are space-time variables and the k=(k^{\mu}) are their conjugate wave vector-frequency variables. The procedure is first applied to the variables (x,k) and produces canonically conjugate essentially  self-adjoint operators. It is next applied to the metric field g_{\mu\nu}(x) of general relativity and yields regularised  semi-classical phase space portraits of it.

S.Katsanevas
Detecting Gravitational Waves at the Moon

Astrophysical observations are largely based on electromagnetic signals still read with the Maxwellian massless and linear theory, possibly an approximation of a larger theory, as Newtonian gravity is for Einsteinian gravity in weak fields. Photons are the sole free massless particles in the Standard-Model (SM). Apart from massive formalisms (de Broglie-Proca, Bopp, Stueckelberg and others), the SM Extension dresses the photon of a mass dependent from the Lorentz-Poincaré symmetry violation.

The Second Joint ECFA-NuPECC-ApPEC Seminar (JENAS) will be held from May 3rd to 6th, 2022 in Madrid  
The seminar is a prestigious joint meeting of particle, nuclear and astroparticle physics scientific communities exploring synergies and highlighting recent achievements and challenges.

The participants represent scientists of the three communities, the funding agencies (important for our field) as well as big international projects and collaborations. 

In this seminar I will present the first direct numerical simulation of gravitational wave turbulence (Galtier & Nazarenko, PRL 127, 131101, 2021). General relativity equations are solved numerically in a periodic box with a diagonal metric tensor depending on two space coordinates only (Hadad-Zakharov metric) and with an additional small-scale