703 research outputs found
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 and SU(n) for all 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
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