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

A real-time compact monitor for environmental radiation: Cosmic rays and radioactivity

We report here about the possibility of using a compact scintillation NaI(Tl) detector, long-term stable and reliable, to monitor separately the components of the environmental radiation, i.e. in the energy range 0.28–2.8 MeV, due to very low energy secondary (Ultrasoft) cosmic radiation and radioactivity, airborne and from environment matter. We suggest some procedures to accomplish time variation analysis, by using a sample of data collected in Bologna

Silicon Photo-Multiplier radiation hardness tests with a beam controlled neutron source

We report radiation hardness tests performed at the Frascati Neutron Generator on silicon Photo-Multipliers, semiconductor photon detectors built from a square matrix of avalanche photo-diodes on a silicon substrate. Several samples from different manufacturers have been irradiated integrating up to 7x10^10 1-MeV-equivalent neutrons per cm^2. Detector performances have been recorded during the neutron irradiation and a gradual deterioration of their properties was found to happen already after an integrated fluence of the order of 10^8 1-MeV-equivalent neutrons per cm^2.Comment: 7 pages, 6 figures, Submitted to Nucl. Inst. Meth.

4-Dimensional BF Theory as a Topological Quantum Field Theory

Starting from a Lie group G whose Lie algebra is equipped with an invariant nondegenerate symmetric bilinear form, we show that 4-dimensional BF theory with cosmological term gives rise to a TQFT satisfying a generalization of Atiyah's axioms to manifolds equipped with principal G-bundle. The case G = GL(4,R) is especially interesting because every 4-manifold is then naturally equipped with a principal G-bundle, namely its frame bundle. In this case, the partition function of a compact oriented 4-manifold is the exponential of its signature, and the resulting TQFT is isomorphic to that constructed by Crane and Yetter using a state sum model, or by Broda using a surgery presentation of 4-manifolds.Comment: 15 pages in LaTe

Preliminary test results on the new electronic readout of the YAP(S)PET small animal scanner

A small animal PET-SPECT scanner (YAP-(S)PET) prototype was built at the Physics Department of the University of Ferrara and is presently being used at the Nuclear Medicine Department for radiopharmaceutical studies on rats. The first YAP-(S)PET prototype shows very good performances, but needs some improvements before it can be used for intensive radiopharmaceutical research. The main problem of the actual prototype is its heavy electronics, based on NIM and CAMAC standard modules. For this reason a new, compact readout electronics was developed and tested. The results of a first series of tests made on the first prototype will be presented in this paper

Unsuspected Involvement of Spinal Cord in Alzheimer Disease

Objective: Brain atrophy is an established biomarker for dementia, yet spinal cord involvement has not been investigated to date. As the spinal cord is relaying sensorimotor control signals from the cortex to the peripheral nervous system and vice-versa, it is indeed a very interesting question to assess whether it is affected by atrophy due to a disease that is known for its involvement of cognitive domains first and foremost, with motor symptoms being clinically assessed too. We, therefore, hypothesize that in Alzheimer’s disease (AD), severe atrophy can affect the spinal cord too and that spinal cord atrophy is indeed an important in vivo imaging biomarker contributing to understanding neurodegeneration associated with dementia. Methods: 3DT1 images of 31 AD and 35 healthy control (HC) subjects were processed to calculate volume of brain structures and cross-sectional area (CSA) and volume (CSV) of the cervical cord [per vertebra as well as the C2-C3 pair (CSA23 and CSV23)]. Correlated features (ρ > 0.7) were removed, and the best subset identified for patients’ classification with the Random Forest algorithm. General linear model regression was used to find significant differences between groups (p ≤ 0.05). Linear regression was implemented to assess the explained variance of the Mini-Mental State Examination (MMSE) score as a dependent variable with the best features as predictors. Results: Spinal cord features were significantly reduced in AD, independently of brain volumes. Patients classification reached 76% accuracy when including CSA23 together with volumes of hippocampi, left amygdala, white and gray matter, with 74% sensitivity and 78% specificity. CSA23 alone explained 13% of MMSE variance. Discussion: Our findings reveal that C2-C3 spinal cord atrophy contributes to discriminate AD from HC, together with more established features. The results show that CSA23, calculated from the same 3DT1 scan as all other brain volumes (including right and left hippocampi), has a considerable weight in classification tasks warranting further investigations. Together with recent studies revealing that AD atrophy is spread beyond the temporal lobes, our result adds the spinal cord to a number of unsuspected regions involved in the disease. Interestingly, spinal cord atrophy explains also cognitive scores, which could significantly impact how we model sensorimotor control in degenerative diseases with a primary cognitive domain involvement. Prospective studies should be purposely designed to understand the mechanisms of atrophy and the role of the spinal cord in AD