Spectral theory of a mathematical model in Quantum Field Theory for any spin

In this paper we use the formalism of S.Weinberg in order to construct a mathematical model based on the weak decay of hadrons and nuclei. In particular we consider a model which generalizes the weak decay of the nucleus of the cobalt. We associate with this model a Hamiltonian with cutoffs in a Fock space. The Hamiltonian is self-adjoint and has an unique ground state. By using the commutator theory we get a limiting absorption principle from which we deduce that the spectrum of the Hamiltonian is absolutely continuous above the energy of the ground state and below the first threshold.Comment: A subsection revise

A mathematical model for the Fermi weak interactions

We consider a mathematical model of the Fermi theory of weak interactions as patterned according to the well-known current-current coupling of quantum electrodynamics. We focuss on the example of the decay of the muons into electrons, positrons and neutrinos but other examples are considered in the same way. We prove that the Hamiltonian describing this model has a ground state in the fermionic Fock space for a sufficiently small coupling constant. Furthermore we determine the absolutely continuous spectrum of the Hamiltonian and by commutator estimates we prove that the spectrum is absolutely continuous away from a small neighborhood of the thresholds of the free Hamiltonian. For all these results we do not use any infrared cutoff or infrared regularization even if fermions with zero mass are involved

Weak interactions in a background of a uniform magnetic field. A mathematical model for the inverse beta decay.I

In this paper we consider a mathematical model for the inverse beta decay in a uniform magnetic field. With this model we associate a Hamiltonian with cutoffs in an appropriate Fock space. No infrared regularization is assumed. The Hamiltonian is selfadjoint and has a ground state. We study its essential spectrum and determine its spectrum. Conditions for uniqueness of ground state are given. The coupling constant is supposed suffciently small.Comment: The proof of theorem 4.4 is not corrected in this preprin

Detection of Jovian seismic waves: a new probe of its interior structure

Knowledge of Jupiter's deep interior would provide unique constraints on the formation of the Solar System. Measurement of its core mass and global composition would shed light on whether the planet formed by accretion or by direct gravitational collapse. At present, the inner structure of Jupiter is poorly constrained and seismology, which consists of identifying acoustic eigenmodes, offers a way to directly measure its deep sound speed profile, and thus its physical properties. Seismology of Jupiter has been considered since the mid 1970s, but hitherto the various attempts to detect global modes led, at best, to ambiguous results. We report the detection of global modes of Jupiter, based on radial velocity measurements performed with the SYMPA Fourier spectro-imager. The global seismic parameters that we measure include the frequency of maximum amplitude 1213+/-50 \mu Hz, the mean large frequency spacing between radial harmonics 155.3+/-2.2 \mu Hz and the mode maximum amplitude 49 (-10/+8) cm/s, all values that are consistent with current models of Jupiter. This result opens the way to the investigation of the inner structure of the Solar System's giant planets based on seismology techniques.Comment: Accepted in Astronomy & Astrophysics (8 pages, 9 figures