Reduction of Lie--Jordan algebras: Quantum

In this paper we present a theory of reduction of quantum systems in the presence of symmetries and constraints. The language used is that of Lie--Jordan Banach algebras, which are discussed in some detail together with spectrum properties and the space of states. The reduced Lie--Jordan Banach algebra is characterized together with the Dirac states on the physical algebra of observables

The Schwinger Representation of a Group: Concept and Applications

The concept of the Schwinger Representation of a finite or compact simple Lie group is set up as a multiplicity-free direct sum of all the unitary irreducible representations of the group. This is abstracted from the properties of the Schwinger oscillator construction for SU(2), and its relevance in several quantum mechanical contexts is highlighted. The Schwinger representations for $SU(2), SO(3)$ and SU(n) for all $n$ are constructed via specific carrier spaces and group actions. In the SU(2) case connections to the oscillator construction and to Majorana's theorem on pure states for any spin are worked out. The role of the Schwinger Representation in setting up the Wigner-Weyl isomorphism for quantum mechanics on a compact simple Lie group is brought out.Comment: Latex, 17 page

The Hamilton-Jacobi Formalism for Higher Order Field Theories

We extend the geometric Hamilton-Jacobi formalism for hamiltonian mechanics to higher order field theories with regular lagrangian density. We also investigate the dependence of the formalism on the lagrangian density in the class of those yelding the same Euler-Lagrange equations.Comment: 25 page

The low-mass population of the Rho Ophiuchi molecular cloud

Star formation theories are currently divergent regarding the fundamental physical processes that dominate the substellar regime. Observations of nearby young open clusters allow the brown dwarf (BD) population to be characterised down to the planetary mass regime, which ultimately must be accommodated by a successful theory. We hope to uncover the low-mass population of the Rho Ophiuchi molecular cloud and investigate the properties of the newly found brown dwarfs. We use near-IR deep images (reaching completeness limits of approximately 20.5 mag in J, and 18.9 mag in H and Ks) taken with the Wide Field IR Camera (WIRCam) at the Canada France Hawaii Telescope (CFHT) to identify candidate members of Rho Oph in the substellar regime. A spectroscopic follow-up of a small sample of the candidates allows us to assess their spectral type, and subsequently their temperature and membership. We select 110 candidate members of the Rho Ophiuchi molecular cloud, from which 80 have not previously been associated with the cloud. We observed a small sample of these and spectroscopically confirm six new brown dwarfs with spectral types ranging from M6.5 to M8.25

Fire and Explosion Risk Assessment: Application to the Fine Chemicals Industry

The "so-called" Seveso III directive (Directive 2012/18/EU) impose to plant managers to perform a detailed risk assessment and to adopt adequate protection measures in the case their facility is included among those considered subjected to Major Accident, i.e., if the amount of hazardous substances stocked and handled within it is superior to defined threshold limits. Fire risk evaluation needs to consider each plant's complexity and the different regulations and codes it is subjected to. Meanwhile, a thorough approach is required, which does not base itself uniquely on qualitative methods (such as checklists) or semi-quantitative (such as fire load-based approach) but should consider these latter as starting processes to develop a more comprehensive evaluation. Besides this, accident scenarios associated with chemical plants may differ significantly, according to the substances handled, the activities and processes implemented: Typically, they could range from small to medium scale in terms of consequences, depending on the impact on human operators and structures. Several "risk screening" methods exist, differing from their fields of applications and limitations, as detailed by Danzi et al. (2018). The SWandHI methodology was developed by Khan et al. (2001). It is a fast tool that allows to identify the most hazardous units in chemical process plants, underline the criticalities associated with different substances, processes, and operations, evaluate the effectiveness of the protection measures in place, compare the risk level attributed to different chemical processes, define the adequate additional measures to reduce the risk to an acceptable level. In this work, the SWandHI method (with the modifications proposed in Danzi et al. 2018) is adopted as a preliminary risk screening approach in the production departments of a fine chemicals production plant in Northern Italy, which is identified as a relevant case study due to the heterogeneity of substances and chemical processes available. This study aims to verify the applicability and effectiveness of SWandHI when adopted in the evaluation of fire risk of "medium-size" plants, or "just below" Seveso III thresholds facilities (which could be considered as a majority in Italy), and to identify the prevention and protection measures most suitable to be implemented in this context to mitigate the fire and explosion scenario. The risk assessment conducted in this work will contribute, with further applications, to: (a) the tuning and calibration of the SWandHI method to "medium" scale chemical industrial realities; (b) the definition of a standard procedure of fire and explosion risk screening through SWandHI; (c) the implementation of the validated method into the Italian fire risk regulations

A variational principle for volume-preserving dynamics

We provide a variational description of any Liouville (i.e. volume preserving) autonomous vector fields on a smooth manifold. This is obtained via a ``maximal degree'' variational principle; critical sections for this are integral manifolds for the Liouville vector field. We work in coordinates and provide explicit formulae

Reduction of Lie-Jordan algebras: Classical

In this paper we present a unified algebraic framework to discuss the reduction of classical and quantum systems. The underlying algebraic structure is a Lie-Jordan algebra supplemented, in the quantum case, with a Banach structure. We discuss the reduction by symmetries, by constraints as well as the possible, non trivial, combinations of both. We finally introduce a new, general framework to perform the reduction of physical systems in an algebraic setup