Identification of Berezin-Toeplitz deformation quantization

We give a complete identification of the deformation quantization which was obtained from the Berezin-Toeplitz quantization on an arbitrary compact Kaehler manifold. The deformation quantization with the opposite star-product proves to be a differential deformation quantization with separation of variables whose classifying form is explicitly calculated. Its characteristic class (which classifies star-products up to equivalence) is obtained. The proof is based on the microlocal description of the Szegoe kernel of a strictly pseudoconvex domain given by Boutet de Monvel and Sjoestrand.Comment: 26 page

Wigner Trajectory Characteristics in Phase Space and Field Theory

Exact characteristic trajectories are specified for the time-propagating Wigner phase-space distribution function. They are especially simple---indeed, classical---for the quantized simple harmonic oscillator, which serves as the underpinning of the field theoretic Wigner functional formulation introduced. Scalar field theory is thus reformulated in terms of distributions in field phase space. Applications to duality transformations in field theory are discussed.Comment: 9 pages, LaTex2

Romano, Santi

Santi Romano was born in Palermo, Sicily on January 31, 1875. His origins had a notable impact on his legal training, as Palermo was the cradle of a host of renewed legal studies that changed once and for all the way of approaching public law in Italy. His teacher, Vittorio Emanuele Orlando, was both a leading statesman and an innovator of the notion and practice of public and administrative law. The young Romano contributed to a seminal collection of volumes, edited by Orlando, devoted to Italian administrative law, Primo trattato completo di diritto amministrativo italiano (First Complete Treatise on Italian Administrative Law), published between 1900 and 1915. The importance Orlando and his many collaborators attached to such a monumental scholarly enterprise should not go unnoticed: in his preface to the first volume, Orlando emphasized his and the other contributors’ conscious, and eventually successful, attempt at constructing an Italian school of public law. This collection of writings, he claimed, was the necessary counterpoint to the growing expansion of the state’s competences in the public realm. While in the past, Italian scholars had been heavily influenced by the French lawyers who had been working and mulling over the Code Napoléon and, subsequently, by the German pandectists, Orlando insisted that the specialization and evolution of the Italian state called for a full-fledged “homegrown” scholarly apparatus. After obtaining his degree at the University of Palermo, Romano wholeheartedly adhered to this ambitious project

A Path Integral Approach To Noncommutative Superspace

A path integral formula for the associative star-product of two superfields is proposed. It is a generalization of the Kontsevich-Cattaneo-Felder's formula for the star-product of functions of bosonic coordinates. The associativity of the star-product imposes certain conditions on the background of our sigma model. For generic background the action is not supersymmetric. The supersymmetry invariance of the action constrains the background and leads to a simple formula for the star-product.Comment: Latex 13 pages. v2: references and footnotes adde

Direct Detection of Electroweak-Interacting Dark Matter

Assuming that the lightest neutral component in an SU(2)L gauge multiplet is the main ingredient of dark matter in the universe, we calculate the elastic scattering cross section of the dark matter with nucleon, which is an important quantity for the direct detection experiments. When the dark matter is a real scalar or a Majorana fermion which has only electroweak gauge interactions, the scattering with quarks and gluon are induced through one- and two-loop quantum processes, respectively, and both of them give rise to comparable contributions to the elastic scattering cross section. We evaluate all of the contributions at the leading order and find that there is an accidental cancellation among them. As a result, the spin-independent cross section is found to be O(10^-(46-48)) cm^2, which is far below the current experimental bounds.Comment: 19 pages, 7 figures, published versio