Affine bundles are affine spaces over modules

We show that the category of affine bundles over a smooth manifold M is equivalent to the category of affine spaces modelled on projective finitely generated C^\infty(M)-modules. Using this equivalence of categories, we are able to give an alternate proof of the main result of [13], showing that the characterization of vector bundles by means of their Lie algebras of homogeneous differential operators also holds for vector bundles of rank 1 and over any base manifolds.Comment: 13 page

Natural and Projectively Invariant Quantizations on Supermanifolds

The existence of a natural and projectively invariant quantization in the sense of P. Lecomte [Progr. Theoret. Phys. Suppl. (2001), no. 144, 125-132] was proved by M. Bordemann [math.DG/0208171], using the framework of Thomas-Whitehead connections. We extend the problem to the context of supermanifolds and adapt M. Bordemann's method in order to solve it. The obtained quantization appears as the natural globalization of the $\mathfrak{pgl}({n+1|m})$-equivariant quantization on ${\mathbb{R}}^{n|m}$ constructed by P. Mathonet and F. Radoux in [arXiv:1003.3320]. Our quantization is also a prolongation to arbitrary degree symbols of the projectively invariant quantization constructed by J. George in [arXiv:0909.5419] for symbols of degree two

Quantifications en supergéométrie

Le poster présente de façon vulgarisée certaines idées sous-jacentes à la recherche de quantifications invariantes en supergéométrie

Affine bundles are affine spaces

We show that the category of affine bundles over a smooth manifold M is equivalent to that of affine spaces modeled on locally free modules over the algebra of smooth functions on M

Geodesics on a supermanifold and projective equivalence of super connections

We investigate the concept of projective equivalence of connections in supergeometry. To this aim, we propose a definition for (super) geodesics on a supermanifold in which, as in the classical case, they are the projections of the integral curves of a vector field on the tangent bundle: the geodesic vector field associated with the connection. Our (super) geodesics possess the same properties as the in the classical case: there exists a unique (super) geodesic satisfying a given initial condition and when the connection is metric, our supergeodesics coincide with the trajectories of a free particle with unit mass. Moreover, using our definition, we are able to establish Weyl's characterization of projective equivalence in the super context: two torsion-free (super) connections define the same geodesics (up to reparametrizations) if and only if their difference tensor can be expressed by means of a (smooth, even, super) 1-form.Comment: 20 page

On a Lie Algebraic Characterization of Vector Bundles

We prove that a vector bundle $\pi : E \to M$ is characterized by the Lie algebra generated by all differential operators on $E$ which are eigenvectors of the Lie derivative in the direction of the Euler vector field. Our result is of Pursell-Shanks type but it is remarkable in the sense that it is the whole fibration that is characterized here. The proof relies on a theorem of [Lecomte P., J. Math. Pures Appl. (9) 60 (1981), 229-239] and inherits the same hypotheses. In particular, our characterization holds only for vector bundles of rank greater than 1

On osp(p+1,q+1|2r)-equivariant quantizations

We investigate the concept of equivariant quantization over the superspace R^{p+q|2r}, with respect to the orthosymplectic algebra osp(p+1,q+1|2r). Our methods and results vary upon the superdimension p+q-2r. When the superdimension is nonzero, we manage to obtain a result which is similar to the classical theorem of Duval, Lecomte and Ovsienko: we prove the existence and uniqueness of the equivariant quantization except in some resonant situations. To do so, we have to adapt their methods to take into account the fact that the Casimir operator of the orthosymplectic algebra on supersymmetric tensors is not always diagonalizable, when the superdimension is negative and even. When the superdimension is zero, the situation is always resonant, but we can show the existence of a one-parameter family of equivariant quantizations for symbols of degree at most two.Comment: 17 page

Créer son document écrit avec LaTeX

LaTeX est un traitement de texte orienté contenu, gratuit et qui produit des documents de qualité typographique irréprochable. LaTeX nécessite un petit apprentissage, mais il s’agit d’un investissement dont on récolte très vite les fruits. Le document présente le fonctionnement général de LaTeX, les notions de base nécessaires à la rédaction d'un premier document de type article et comment devenir autonome dans l’apprentissage

Investigation of compact power amplifier cells at THz frequencies using InGaAs mHEMT technology

In this paper a design approach for compact power amplifier cells at frequencies around and above 300 GHz is presented, using a 35nm InGaAs mHEMT technology. Up to 8-finger common-source (CS) and cascode devices are developed based on 2-finger multiport models without feeding structures. Two power amplifier MMICs are presented with more than 15 dB measured small-signal gain between 290 – 335 GHz. 6.8 – 8.6-dBm output power is reported for the frequency range of 280 – 320 GHz, which is state-of-the-art for InGaAs based mHEMT technologies at these frequencies. Due to the compact CS and cascode cells, the required width of the PA core is significantly reduced, achieving high output power levels per required chip width and enabling further parallelization