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

A Characterization of Binary Bent Functions

AbstractA recent paper by Carlet introduces a general class of binary bent functions on (GF(2))n(neven) whose elements are expressed by means of characteristic functions (indicators) of (n/2)-dimensional vector-subspaces of (GF(2))n. An extended version of this class is introduced in the same paper; it is conjectured that this version is equal to the whole class of bent functions. In the present paper, we prove that this conjecture is true

Banten sebelum zaman Islam: kajian arkeologi di Banten Girang 932?-1526

Pengetahuan tentang sejarah Banten itu pertama-tama dirintis oleh karya Hoesein Djajadiningrat yang diterbitkan pada tahun 1913 di Haarlem dengan judul: Critische beschouwing van de Sajarah Banten Bijdrage ter kenschetsing van de Javaansche geschiedschrijving. Dengan kajian itu, Hoesein Djajadiningrat yang seorang putra Banten juga merupakan orang pertama yang mendapat gelar doktor di bidang sastra timur di Negeri Belanda

Villes portuaires et États côtiers en Insulinde

Claude Guillot, directeur d’études Compte rendu non communiqué