Highlights of Symmetry Groups

The concepts of symmetry and symmetry groups are at the heart of several developments in modern theoretical and mathematical physics. The present paper is devoted to a number of selected topics within this framework: Euclidean and rotation groups; the properties of fullerenes in physical chemistry; Galilei, Lorentz and Poincare groups; conformal transformations and the Laplace equation; quantum groups and Sklyanin algebras. For example, graphite can be vaporized by laser irradiation, producing a remarkably stable cluster consisting of 60 carbon atoms. The corresponding theoretical model considers a truncated icosahedron, i.e. a polygon with 60 vertices and 32 faces, 12 of which are pentagonal and 20 hexagonal. The Carbon 60 molecule obtained when a carbon atom is placed at each vertex of this structure has all valences satisfied by two single bonds and one double bond. In other words, a structure in which a pentagon is completely surrounded by hexagons is stable. Thus, a cage in which all 12 pentagons are completely surrounded by hexagons has optimum stability. On a more formal side, the exactly solvable models of quantum and statistical physics can be studied with the help of the quantum inverse problem method. The problem of enumerating the discrete quantum systems which can be solved by the quantum inverse problem method reduces to the problem of enumerating the operator-valued functions that satisfy an equation involving a fixed solution of the quantum Yang--Baxter equation. Two basic equations exist which provide a systematic procedure for obtaining completely integrable lattice approximations to various continuous completely integrable systems. This analysis leads in turn to the discovery of Sklyanin algebras.Comment: Plain Tex with one figur

Twistors and Spin 3/2 Potentials in Quantum Gravity

Local boundary conditions involving field strengths and the normal to the boundary, originally studied in anti-de Sitter space-time, have been recently considered in one-loop quantum cosmology. This paper derives the conditions under which spin-lowering and spin-raising operators preserve these local boundary conditions on a 3-sphere for fields of spin 0,1/2,1,3/2 and 2. Moreover, the two-component spinor analysis of the four potentials of the totally symmetric and independent field strengths for spin 3/2 is applied to the case of a 3-sphere boundary. It is shown that such boundary conditions can only be imposed in a flat Euclidean background, for which the gauge freedom in the choice of the potentials remains. Alternative boundary conditions for supergravity involving the spinor-valued 1-forms for gravitinos and the normal to the boundary are also studied.Comment: 20 pages, plain-tex, recently appearing in: Twistor Theory, edited by Stephen Huggett (Marcel Dekker, New York, 1994). The authors apologize for the delay in circulating the paper, which was due to technical problems now fixe

Classical brackets for dissipative systems

We show how to write a set of brackets for the Langevin equation, describing the dissipative motion of a classical particle, subject to external random forces. The method does not rely on an action principle, and is based solely on the phenomenological description of the dissipative dynamics as given by the Langevin equation. The general expression for the brackets satisfied by the coordinates, as well as by the external random forces, at different times, is determined, and it turns out that they all satisfy the Jacobi identity. Upon quantization, these classical brackets are found to coincide with the commutation rules for the quantum Langevin equation, that have been obtained in the past, by appealing to microscopic conservative quantum models for the friction mechanism.Comment: Latex file, 8 pages, prepared for the Conference Spacetime and Fundamental Interactions: Quantum Aspects, Vietri sul Mare, Italy, 26-31 May 200

Detection of trace elements in the bivalve Ruditapes decussatus from Sardinian coastal lagoons: effects on food safety and pathological findings in target organs

Shellfish can bioaccumulate toxic metals due to their ability to concentrate inorganic contaminants. Since biomonitoring by using bivalve molluscs is currently considered one of the most effective approaches for assessing the degree of pollution of brackish environments, the aims of this PhD thesis were: a) to detect the content of trace elements in the Grooved carpet shell Ruditapes decussatus collected in Sardinian coastal lagoons (Italy) and their effects on food safety; b) to evaluate the pathological findings in its target organs. The concentration of 16 trace elements (Al, Ag, As, Cd, Co, Cr, Cu, Fe, Hg, Mn, Ni, Pb, Se, Sn, Tl and Zn) was quantified. The legal limits set by European Regulations for Cd, Hg and Pb were never exceeded. Unexpectedly high values for Al and Fe were found. A total of six histopathological alterations were analysed in the digestive gland, gills and kidney following a weighted condition indices approach. Gills show the highest prevalence of lesions than digestive gland, followed by kidney. The clam R. decussatus confirmed the capacity of bivalves as suitable bioindicators of trace elements pollution. The determination of trace elements combined with histopathological analysis, should be a powerful tool in environmental monitoring plans. It is useful for understanding directly the health status of the marine organisms and indirectly the impact which different anthropogenic activities have on shellfish harvested in coastal environments

Variations of Casimir energy from a superconducting transition

We consider a five-layer Casimir cavity, including a thin superconducting film. We show that when the cavity is cooled below the critical temperature for the onset of superconductivity, the sharp variation (in the microwave region) of the reflection coefficient of the film produces a variation in the value of the Casimir energy. Even though the relative variation in the Casimir energy is very small, its magnitude can be comparable to the condensation energy of the superconducting film, and thus causes a significant increase in the value of the critical magnetic field, required to destroy the superconductivity of the film. The proposed scheme might also help clarifying the current controversy about the magnitude of the contribution to Casimir free energy from the TE zero mode, as we find that alternative treatments of this mode strongly affect the shift of critical field.Comment: RevTex 4, 15 pages, 8 figures. Revised version with improved presentation, a brief description of the ALADIN experiment, and a few references adde

Push on a Casimir apparatus in a weak gravitational field

The influence of the gravity acceleration on the regularized energy-momentum tensor of the quantized electromagnetic field between two plane parallel conducting plates is derived. We use Fermi coordinates and work to first order in the constant acceleration parameter. A new simple formula for the trace anomaly is found to first order in the constant acceleration, and a more systematic derivation is therefore obtained of the theoretical prediction according to which the Casimir device in a weak gravitational field will experience a tiny push in the upwards direction.Comment: 14 pages, Plain Tex. Talk given at the 17th SIGRAV Conference on General Relativity and Gravitational Physics, Torino, September 200

Boundary Terms for Massless Fermionic Fields

Local supersymmetry leads to boundary conditions for fermionic fields in one-loop quantum cosmology involving the Euclidean normal to the boundary and a pair of independent spinor fields. This paper studies the corresponding classical properties, i.e. the classical boundary-value problem and boundary terms in the variational problem. Interestingly, a link is found with the classical boundary-value problem when spectral boundary conditions are imposed on a 3-sphere in the massless case. Moreover, the boundary term in the action functional is derived.Comment: 8 pages, plain-tex, recently appearing in Foundations of Physics Letters, volume 7, pages 303-308, year 199

Ultrabiomicroscopy anterior segment evaluation of ocular contusive trauma caused by pressurized bottled drink caps. a case report

We report the case of a patient presented to the emergency department because of a contu-sive trauma from a pressurized bottled drink cap. During the visit, the patient indicated that he had been hit in his left eye by a cork while he was opening a sparkling wine bottle. He underwent a total ophthalmology examination. He had an important reduction of visual acuity, corneal swelling, Descemet’s folds, and hyphema. Therefore, we decided to perform ultrabio-microscopy (UBM) of the anterior segment to study the endothelial damage and Descemet’s membrane. UBM images confirmed the direct biomicroscopy, highlighting the damaged loca-tion