Q-spaces and the Foundations of Quantum Mechanics

Our aim in this paper is to take quite seriously Heinz Post’s claim that the non-individuality and the indiscernibility of quantum objects should be introduced right at the start, and not made a posteriori by introducing symmetry conditions. Using a different mathematical framework, namely, quasi-set theory, we avoid working within a label-tensor-product-vector-space-formalism, to use Redhead and Teller’s words, and get a more intuitive way of dealing with the formalism of quantum mechanics, although the underlying logic should be modified. We build a vector space with inner product, the Q-space, using the non-classical part of quasi-set theory, to deal with indistinguishable elements. Vectors in Q-space refer only to occupation numbers and permutation operators act as the identity operator on them, reflecting in the formalism the fact of unobservability of permutations. Thus, this paper can be regarded as a tentative to follow and enlarge Heinsenberg’s suggestion that new phenomena require the formation of a new “closed” (that is, axiomatic) theory, coping also with the physical theory’s underlying logic and mathematics. G. Domenech is a fellow of the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina. D. Krause is a fellow of the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Brazil.     

The Heterotic Supersymmetric Sigma Model in the Canonical Exterior Formalism

Starting from a classical 2D superconformal theory described by the Wess–Zumino–Witten action, the canonical exterior formalism on group manifold for the heterotic supersymmetric sigma model is constructed. The motion equations of the dynamical field and the constraints are found and analyzed from the geometric point of view. It can be seen how the use of the canonical exterior formalism is more adequate and simple because of its manifest covariance in all the steps. The relationship between the form brackets defined in the canonical exterior formalism and the Poisson-brackets is written. Later on, the Dirac-brackets are written by using the second class constraints provided by the canonical exterior formalism. As it can be seen the canonical exterior formalism allows to show how the canonical quantization of the heterotic supersymmetric sigma model is facilitated. Member of the Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina.     

A Discussion on Particle Number and Quantum Indistinguishability

The concept of individuality in quantum mechanics shows radical differences from the concept of individuality in classical physics, as E. Schr?dinger pointed out in the early steps of the theory. Regarding this fact, some authors suggested that quantum mechanics does not possess its own language, and therefore, quantum indistinguishability is not incorporated in the theory from the beginning. Nevertheless, it is possible to represent the idea of quantum indistinguishability with a first-order language using quasiset theory (Q). In this work, we show that Q cannot capture one of the most important features of quantum non-individuality, which is the fact that there are quantum systems for which particle number is not well defined. An axiomatic variant of Q, in which quasicardinal is not a primitive concept (for a kind of quasisets called finite quasisets), is also given. This result encourages the searching of theories in which the quasicardinal, being a secondary concept, stands undefined for some quasisets, besides showing explicitly that in a set theory about collections of truly indistinguishable entities, the quasicardinal needs not necessarily be a primitive concept. Graciela Domenech — Fellow of the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET).     

Diffusion of Ta in α-Ti

The diffusion of Ta in the hcp (α) phase of high-purity Ti (99.99%) was studied at different temperatures from 911 K up to 1123 K. The Rutherford Backscattering Spectrometry (RBS) and Heavy Ion RBS (HIRBS) techniques were used to obtain the penetration profiles. The evolution of the diffusion coefficient, D, as a function of temperature follows prediction of the Arrhenius law. The activation energy of the diffusion process is (318±7)kJ/mol, similar to that corresponding to self-diffusion in α-Ti. On the other hand, the measured values of D are systematically lower than those corresponding to self-diffusion by a factor of approximately 5. This reduction could be explained by taking into account the mass difference between Ta and Ti. An increase of the diffusion coefficient was measured when the diffusion proceeds on a less pure Ti (99.9%) matrix. This increment is higher at lower temperatures. Received: 12 November 2001 / Accepted: 12 March 2002 / Published online: 5 July 2002 RID="*" ID="*" RID="*" ID="*" RID="**" ID="**"Corresponding author. Fax: +54-11/6772-7362, E-mail: dyment@cnea.gov.ar RID="*" ID="*"Members of the Carrera del Investigador Científico del Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina     

Convolution of Ultradistributions,Field Theory,Lorentz Invariance and Resonances

In this work, a general definition of convolution between two arbitrary Ultradistributions of Exponential type (UET) is given. The product of two arbitrary UET is defined via the convolution of its corresponding Fourier Transforms. Some examples of convolution of two UET are given. Expressions for the Fourier Transform of spherically symmetric (in Euclidean space) and Lorentz invariant (in Minkowskian space) UET in term of modified Bessel distributions are obtained (Generalization of Bochner’s theorem). The generalization to UET of dimensional regularization in configuration space is obtained in both, Euclidean and Minkowskian spaces As an application of our formalism, we give a solution to the question of normalization of resonances in Quantum Mechanics. General formulae for convolution of even, spherically symmetric and Lorentz invariant UET are obtained and several examples of application are given. This work was partially supported by Consejo Nacional de Investigaciones Científicas and Comisión de Investigaciones Científicas de la Pcia. de Buenos Aires; Argentina.     

Renormalization group calculation for cells with inequivalent spins

We have considered a real-space renormalization group transformation for a bidimensional Ising model, carrying out approximate calculations for cells where site spins do not play the same role. The dependence on the ratio between the number of intercell and intracell nearest-neighbour interactions has also been discussed.Fellow of the Consejo Nacional de Investigaciones Científicas y Técnicas de Argentina.Fellow of the Comisión de Investigaciones Científicas de la Provincia de Buenos Aires, Argentina.     

Two-Dimensional Supergravity in the Canonical Exterior Formalism

The main features of the different linear gravity theories are reviewed. In particular, the supersymmetric extension of the Jackiw–Teitelboim (1+1) linear gravity is considered in detail within the canonical exterior formalism. In this context, the role of the several fields are analyzed. The constraints and the field equation are found. Finally, this supergravity model is treated in the second-order formalism.Member of the Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina.     

A comment on spiral motions in projective relativity

Astronomical evidence has been inadequately invoked to support projective relativity. The spiral structure cannot be explained just by the existence of spiral orbits, and the use of Oort's constant to support the theory is also a missunderstanding. Besides, some mathematical inaccuracies make the application invalid.On a fellowship from the Consejo Nacional de Investigaciones Científicas y Técnicas de la República Argentina.     

A relation between the Szekeres quasispherical gravitational collapse solution and the Robinson-Trautman metrics

A form of the Robinson-Trautman metric for pure radiation is obtained by applying a limiting procedure to the quasispherical gravitational collapse solution of Szekeres. The procedure can be interpreted as that of allowing the particles making up the dust in the Szekeres solution to become massless.Research supported in part by a scholarship awarded to the author by the Consejo Nacional de Investigaciones Cintíficas y Técnicas of Argentina.     

Maximum mass of a Neutron star in metric theories of gravitation

A method is proposed of finding approximately the equilibrium configurations of nonrotating neutron stars without choosing any particular field equation for the metric. The method consists in choosing interpolation functions for the metric coefficients inside the star and matching them to that of the external metric at the body surface. In particular, the maximum mass a neutron star may have against gravitational collapse is studied, and a good agreement is found when compared with general relativistic results.On a fellowship from the Consejo Nacional de Investigaciones, Científicas y Técnicas de la República Argentina.     

Study of recombination reactions of particles adsorbed on fractal and multifractal substrata

Recombination reactions of adsorbed particles on fractal and multifractal media are discussed within the framework of the random walk arguments. Theoretical results, which predict anomalous reaction orderX>2 in the low coverage regime, are checked by means of Monte Carlo simulations on two-dimensional structures and good agreement is found. Thermal desorption experiments on rough surfaces are simulated by studying temperature programmed reactions on fractal percolating clusters. For this case the simulations giveX≅2.5, i. e. the fractal reaction order is greater than the classical one (X=2). The influence of chemisorbed impurities (poison) on the recombination reaction is also studied and the reaction order is found to increase beyondX=2.5 when increasing the concentration of poison. Isothermal (recombination) desorption from energetically heterogeneous surfaces is simulated on two-dimensional substrata with multifractal distributions of activation energy of diffusion. For this caseX (withX>2) depends on the energetic heterogeneity of the substrata (X=2 for an homogeneous substratum). The obtained results point out that the fractal chemical kinetic behaviour is not only restricted to the low concentration regime, but it also covers the medium coverage regime, i.e. it holds for a monolayer surface coverageθ≦0.4 in fractal percolating clusters. Financially supported by the Consejo Nacional de Investigaciones Cientificas y Técnicas (CONICET) de la República Argentina     

On the post-Newtonian approximation of the Einstein-Cartan-Sciama-Kibble theory

The post-Newtonian approximation of the Einstein-Cartan-Sciama-Kibble or ECSK theory is developed. It is used to obtain a drastic reduction on the density of the source needed to detect the spin. It is also proved that if we know the structure of the source, up to order ¯v, the spin can be detected, and if we know it up to order ¯v² the theory can be verified.Supported by a scholarship from the Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET).     

MGP Versus Kochen–Specker Condition in Hidden Variables Theories

Hidden variables theories} for quantum mechanics are usually assumed to satisfy the KS condition. The Bell–Kochen–Specker theorem then shows that these theories are necessarily contextual. But the KS condition can be criticized from an operational viewpoint, which suggests that a weaker condition (MGP) should be adopted in place of it. This leads one to introduce a class of hidden parameters theories in which contextuality can, in principle, be avoided, since the proofs of the Bell–Kochen–Specker theorem break down. A simple model recently provided by the author for an objective interpretation of quantum mechanics can be looked at as a noncontextual hidden parameters theory, which shows that such theories actually exist.     

On the post-Newtonian approximation of the ECSK theory II

We complete the PNA program for the ECSK theory. We find the general post-Newtonian equations of motion for the source. The different components of the complete affine connection, the torsion, and the energy-momentum tensor, as well as the conservation theorems of the theory, are developed for the case of an ideal fluid with spin in order to find the post-Newtonian trajectories of test particles exterior to the sources distribution. The main results are compared with the corresponding ones of general relativity.Supported by a scholarship from the Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET).     

Electric Fields Gradients at 111In Sites in CdIn2O4 Spinel

The perturbed angular correlation (PAC) technique was applied to study the electric field gradients at ¹¹¹In sites in CdIn₂O₄. The measurements were carried out at temperatures in the range 150–1073 K. The aims of the study were both to characterize the quadrupole interactions of the tracers and to determine the distribution of indium ions among the available sites in the spinel structure. Room temperature measurements corresponding to samples cooled at different rates are also reported. ^aAlso at Comisión de Investigasiones Científicas de la Provincia de Buenos Aires, Argentina.     

The Nonanuclear [Mo(IV){(CN)Fe(III)(3-ethoxy-saldptn)}8]Cl4 Complex Compound Exhibits Multiple Spin Transitions Observed by Mössbauer Spectroscopy

The hyperfine interactions at ¹⁸¹Ta ions on Fe³⁺ sites in α-Fe₂O₃ (hematite) were studied in the temperature range 11–1100 K by means of the perturbed angular correlation (PAC) technique. The ¹⁸¹Hf(β⁻)¹⁸¹Ta probe nuclei were introduced chemically into the sample during the preparation. The hyperfine interaction measurements allow to observe the magnetic phase transition and to characterize the supertransferred hyperfine magnetic field B_hf and the electric field gradient (EFG) at the impurity sites. The angles between B_hf and the principal axes of the EFG were determined. The Morin transition was also observed. The results are compared with those of similar experiments carried out using ¹¹¹Cd probe. ^aAlso at Comisión de Investigaciones Científicas de la Provincia de Buenos Aires, Argentina.     

Perturbed angular correlation study of order– disorder transition in HfW2O8

The perturbed angular correlation (PAC) technique has been used to characterize the degree of atomic order in the neighbourhood of radioactive ¹⁸¹Hf isotopes in HfW₂O₈. PAC measurements were carried out at temperatures between 14 and 723 K. The compound was synthesized starting with the oxides HfO₂ and WO₃, using a method involving ball milling, high temperature annealing and quenching in liquid nitrogen. Fast cooling allows to have the compound at temperatures below 1050 K. The compound has a high degree of stability below such temperature and around 430 K atomic ordering occurs. This transition order–disorder is reversible. ^aAlso at Comisión de Investigasiones Científicas de la Provincia de Buenos Aires, Argentina.     

Observables have No Value: A no-go Theorem for Position and Momentum Observables

The Bell–Kochen–Specker contradiction is presented using continuous observables in infinite dimensional Hilbert space. It is shown that the assumption of the existence of putative values for position and momentum observables for one single particle is incompatible with quantum mechanics.