Image inverse d'un D-module and Newton Polygon)

We show that, under conditions about the microcharacteristic variety of a coherent -module, the Cauchy problem is well-posed in the spaces of formal power series with Gevrey growth. We deduce that the filtration of the Irregularity Sheaf of a holonomic -module, which we defined in a previous work, is preserved under inverse image if some rather general geometric conditions are fullfilled.     

The one particle theory of periodic point interactions

We solve explicitly and without approximation the problem of a quantum-mechanical particle inR ³ subjected to point interactions that are periodic inR ³ with periodicity of the typeZ, Z ², andZ ³. In the first case we get a model of an infinite straight polymer, in the second case we get a model of a monomolecular layer and in the third case we get a model of a crystal. In all three cases the unit cell of the Bravais lattice is allowed to contain any finite number of interaction sites (atomes), placed arbitrarily and with arbitrary interaction strength. In the case: one interaction site per unit cell we find explicit formulas for the resonance bands and energy bands and their corresponding wavefunctions.     

Central decomposition of invariant states applications to the groups of time translations and of euclidean transformations in algebraic field theory

With aC*-algebra with unit andgG _g a homomorphic map of a groupG into the automorphism group ofG, the central measure of a state of is invariant under the action ofG (in the state space of ) iff is -invariant. Furthermore if the pair { ,G} is asymptotically abelian, is ergodic iff is ergodic. Transitive ergodic states (corresponding to transitive central measures) are centrally decomposed into primary states whose isotropy groups form a conjugacy class of subgroups. IfG is locally compact and acts continuously on , the associated covariant representations of { , } are those induced by such subgroups. Transitive states under time-translations must be primary if required to be stable. The last section offers a complete classification of the isotropy groups of the primary states occurring in the central decomposition of euclidean transitive ergodic invariant states.     

Algebraic theory of the chemicall potential in the case of the usual gauge group

For the usual case where the gauge group is a one-dimensional torus, we give an elementary version of the Araki-Haag-Kastler-Takesaki theory of the chemical potential.     

The 1/r expansion for the critical multiple well problem

We consider the critical multiple well problem $$H = - \Delta + \sum\limits_{i = 1}^n {V(x - rx_i )} ,$$ where ?Δ+V(x) has a zero energy resonance. We prove that all eigenvalues and resonances ofH tending to zero as 1/r ² are analytic in 1/r. We give an explicit equation for the lowest nonvanishing coefficient in the 1/r expansion for any of these eigenvalues or resonances and observe thatH has infinitely many resonances tending to zero. Forn=2 andn=3, we compute the coefficients explicitly and forn=2, we also give the next coefficient in the 1/r expansion.     

Constructibilité de de Rham p-adique

We use the theory of special modules to define the category of de Rham p-adic complexes on a smooth scheme over a perfect field and we prove a constructibility criterion implying the first finiteness properties.