Coisotropic submanifolds in Poisson geometry and branes in the Poisson sigma model

General boundary conditions ("branes") for the Poisson sigma model are studied. They turn out to be labeled by coisotropic submanifolds of the given Poisson manifold. The role played by these boundary conditions both at the classical and at the perturbative quantum level is discussed. It turns out to be related at the classical level to the category of Poisson manifolds with dual pairs as morphisms and at the perturbative quantum level to the category of associative algebras (deforming algebras of functions on Poisson manifolds) with bimodules as morphisms. Possibly singular Poisson manifolds arising from reduction enter naturally into the picture and, in particular, the construction yields (under certain assumptions) their deformation quantization.Comment: 21 pages, 2 figures; minor corrections, references updated; final versio

Loop and Path Spaces and Four-Dimensional BF Theories: Connections, Holonomies and Observables

We study the differential geometry of principal G-bundles whose base space is the space of free paths (loops) on a manifold M. In particular we consider connections defined in terms of pairs (A,B), where A is a connection for a fixed principal bundle P(M,G) and B is a 2-form on M. The relevant curvatures, parallel transports and holonomies are computed and their expressions in local coordinates are exhibited. When the 2-form B is given by the curvature of A, then the so-called non-abelian Stokes formula follows. For a generic 2-form B, we distinguish the cases when the parallel transport depends on the whole path of paths and when it depends only on the spanned surface. In particular we discuss generalizations of the non-abelian Stokes formula. We study also the invariance properties of the (trace of the) holonomy under suitable transformation groups acting on the pairs (A,B). In this way we are able to define observables for both topological and non-topological quantum field theories of the BF type. In the non topological case, the surface terms may be relevant for the understanding of the quark-confinement problem. In the topological case the (perturbative) four-dimensional quantum BF-theory is expected to yield invariants of imbedded (or immersed) surfaces in a 4-manifold M.Comment: TeX, 39 page

Radiation Hardness tests with neutron flux on different Silicon photomultiplier devices

Radiation hardness is an important requirement for solid state readout devices operating in high radiation environments common in particle physics experiments. The MEGII experiment, at PSI, Switzerland, investigates the forbidden decay $\mu^+ \to \mathrm{e}^+ \gamma$. Exploiting the most intense muon beam of the world. A significant flux of non-thermal neutrons (kinetic energy $E_k\geq 0.5 ~MeV$) is present in the experimental hall produced along the beamline and in the hall itself. We present the effects of neutron fluxes comparable to the MEGII expected doses on several Silicon PhotoMulitpliers (SiPMs). The tested models are: AdvanSiD ASD-NUV3S-P50 (used in MEGII experiment), AdvanSiD ASD-NUV3S-P40, AdvanSiD ASD-RGB3S-P40, Hamamatsu and Excelitas C30742-33-050-X. The neutron source is the thermal Sub-critical Multiplication complex (SM1) moderated with water, located at the University of Pavia (Italy). We report the change of SiPMs most important electric parameters: dark current, dark pulse frequency, gain, direct bias resistance, as a function of the integrated neutron fluency.Comment: 9 pages, 6 figures. Proceedings from Instrumentation for colliding Beam Physics (INSTR-17) 27-02-2017/03-03-2017 Novosibirsk (R

Four-Dimensional Yang-Mills Theory as a Deformation of Topological BF Theory

The classical action for pure Yang--Mills gauge theory can be formulated as a deformation of the topological $BF$ theory where, beside the two-form field $B$, one has to add one extra-field $\eta$ given by a one-form which transforms as the difference of two connections. The ensuing action functional gives a theory that is both classically and quantistically equivalent to the original Yang--Mills theory. In order to prove such an equivalence, it is shown that the dependency on the field $\eta$ can be gauged away completely. This gives rise to a field theory that, for this reason, can be considered as semi-topological or topological in some but not all the fields of the theory. The symmetry group involved in this theory is an affine extension of the tangent gauge group acting on the tangent bundle of the space of connections. A mathematical analysis of this group action and of the relevant BRST complex is discussed in details.Comment: 74 pages, LaTeX, minor corrections; to be published in Commun. Math. Phy

AKSZ-BV Formalism and Courant Algebroid-induced Topological Field Theories

We give a detailed exposition of the Alexandrov-Kontsevich-Schwarz- Zaboronsky superfield formalism using the language of graded manifolds. As a main illustarting example, to every Courant algebroid structure we associate canonically a three-dimensional topological sigma-model. Using the AKSZ formalism, we construct the Batalin-Vilkovisky master action for the model.Comment: 13 pages, based on lectures at Rencontres mathematiques de Glanon 200

The Relative Space: Space Measurements on a Rotating Platform

We introduce here the concept of relative space, an extended 3-space which is recognized as the only space having an operational meaning in the study of the space geometry of a rotating disk. Accordingly, we illustrate how space measurements are performed in the relative space, and we show that an old-aged puzzling problem, that is the Ehrenfest's paradox, is explained in this purely relativistic context. Furthermore, we illustrate the kinematical origin of the tangential dilation which is responsible for the solution of the Ehrenfest's paradox.Comment: 14 pages, 2 EPS figures, LaTeX, to appear in the European Journal of Physic

On the Observables Describing a Quantum Reference Frame

A reference frame F is described by the element g of the Poincare' group P which connects F with a given fixed frame F_0. If F is a quantum frame, defined by a physical object following the laws of quantum physics, the parameters of g have to be considered as quantum observables. However, these observables are not compatible and some of them, namely the coordinates of the origin of F, cannot be represented by self-adjoint operators. Both these difficulties can be overcome by considering a positive-operator-valued measure (POVM) on P, covariant with respect to the left translations of the group, namely a covariance system. We develop a construction procedure for this kind of mathematical structure. The formalism is also used to discuss the quantum observables measured with respect to a quantum reference frame.Comment: 23 pages, no figure

The Timing Counter of the MEG experiment: calibration and performance

The MEG detector is designed to test Lepton Flavor Violation in the $\mu^+\rightarrow e^+\gamma$ decay down to a Branching Ratio of a few $10^{-13}$. The decay topology consists in the coincident emission of a monochromatic photon in direction opposite to a monochromatic positron. A precise measurement of the relative time $t_{e^+\gamma}$ is crucial to suppress the background. The Timing Counter (TC) is designed to precisely measure the time of arrival of the $e^+$ and to provide information to the trigger system. It consists of two sectors up and down stream the decay target, each consisting of two layers. The outer one made of scintillating bars and the inner one of scintillating fibers. Their design criteria and performances are described.Comment: Presented at the 12th Topical Seminar on Innovative Particle and Radiation Detectors (IPRD10) 7 - 10 June 2010, Siena. Accepted by Nuclear Physics B (Proceedings Supplements) (2011)tal

Design and test of an extremely high resolution Timing Counter for the MEG II experiment: preliminary results

The design and tests of Timing Counter elements for the upgrade of the MEG experiment, MEG II,is presented. The detector is based on several small plates of scintillator with a Silicon PhotoMultipliers dual-side readout. The optimisation of the single counter elements (SiPMs, scintillators, geometry) is described. Moreover, the results obtained with a first prototype tested at the Beam Test Facility (BTF) of the INFN Laboratori Nazionali di Frascati (LNF) are presented.Comment: 10 pages, 7 figures. Presented at the 13th Topical Seminar on Innovative Particle and Radiation Detectors (IPRD13) 7-10 October 2013 Siena, Ital

Shear-Driven Dynamo Waves in the Fully Nonlinear Regime

Large-scale dynamo action is well understood when the magnetic Reynolds number (Rm) is small, but becomes problematic in the astrophysically relevant large Rm limit since the fluctuations may control the operation of the dynamo, obscuring the large-scale behavior. Recent works by Tobias & Cattaneo demonstrated numerically the existence of large-scale dynamo action in the form of dynamo waves driven by strongly helical turbulence and shear. Their calculations were carried out in the kinematic regime in which the back-reaction of the Lorentz force on the flow is neglected. Here, we have undertaken a systematic extension of their work to the fully nonlinear regime. Helical turbulence and large-scale shear are produced self-consistently by prescribing body forces that, in the kinematic regime, drive flows that resemble the original velocity used by Tobias & Cattaneo. We have found four different solution types in the nonlinear regime for various ratios of the fluctuating velocity to the shear and Reynolds numbers. Some of the solutions are in the form of propagating waves. Some solutions show large-scale helical magnetic structure. Both waves and structures are permanent only when the kinetic helicity is non-zero on average