Noncommutative Geometry and Symplectic Field Theory

In this work we study representations of the Poincare group defined over symplectic manifolds, deriving the Klein-Gordon and the Dirac equation in phase space. The formalism is associated with relativistic Wigner functions; the Noether theorem is derived in phase space and an interacting field, including a gauge field, approach is discussed.Comment: To appear in Physics Letters

Plasmid-mediated quinolone resistance (PMQR) and mutations in the topoisomerase genes of Salmonella enterica strains from Brazil

The objective of this study was to identify mutations in the Quinolone Resistance Determining sources Regions (QRDR) of the gyrA, gyrB, parC, and parE genes and to determine if any of the qnr variants or the aac(6')-Ib-cr variant were present in strains of Salmonella spp. isolated in Brazil. A total of 126 Salmonella spp. strains from epidemic (n = 114) and poultry (n = 12) origin were evaluated. One hundred and twelve strains (88.8%) were resistant to nalidixic acid (NAL) and 29 (23.01%) showed a reduced susceptibility to ciprofloxacin (Cip). The mutations identified were substitutions limited to the QRDR of the gyrA gene in the codons for Serine 83, Aspartate 87 and Alanine 131. The sensitivity to NAL seems to be a good phenotypic indication of distinguishing mutated and nonmutated strains in the QRDR, however the double mutation in gyrA did not cause resistance to ciprofloxacin. The qnrA1 and qnrB19 genes were detected, respectively, in one epidemic strain of S. Enteritidis and one strain of S. Corvallis of poultry origin. Despite previous detection of qnr genes in Brazil, this is the first report of qnr gene detection in Salmonella, and also the first detection of qnrB19 gene in this country. The results alert for the continuous monitoring of quinolone resistance determinants in order to minimize the emergence and selection of Salmonella spp. strains showing reduced susceptibility or resistance to quinolones

Non-linear Liouville and Shr\"odinger equations in phase space

Unitary representations of the Galilei group are studied in phase space, in order to describe classical and quantum systems. Conditions to write in general form the generator of time translation and Lagrangians in phase space are then established. In the classical case, Galilean invariance provides conditions for writing the Liouville operator and Lagrangian for non-linear systems. We analyze, as an example, a generalized kinetic equation where the collision term is local and non-linear. The quantum counter-part of such unitary representations are developed by using the Moyal (or star) product. Then a non-linear Schr\"odinger equation in phase space is derived and analyzed. In this case, an association with the Wigner formalism is established, which provides a physical interpretation for the formalism