Addenda and corrections to work done on the path-integral approach to classical mechanics

In this paper we continue the study of the path-integral formulation of classical mechanics and in particular we better clarify, with respect to previous papers, the geometrical meaning of the variables entering this formulation. With respect to the first paper with the same title, we {\it correct} here the set of transformations for the auxiliary variables $\lambda_{a}$. We prove that under this new set of transformations the Hamiltonian ${\widetilde{\cal H}}$, appearing in our path-integral, is an exact scalar and the same for the Lagrangian. Despite this different transformation, the variables $\lambda_{a}$ maintain the same operatorial meaning as before but on a different functional space. Cleared up this point we then show that the space spanned by the whole set of variables ($\phi, c, \lambda,\bar c$) of our path-integral is the cotangent bundle to the {\it reversed-parity} tangent bundle of the phase space ${\cal M}$ of our system and it is indicated as $T^{\star}(\Pi T{\cal M})$. In case the reader feel uneasy with this strange {\it Grassmannian} double bundle, we show in this paper that it is possible to build a different path-integral made only of {\it bosonic} variables. These turn out to be the coordinates of $T^{\star}(T^{\star}{\cal M})$ which is the double cotangent bundle of phase-space.Comment: Title changed, appendix expanded, few misprints fixe

A Proposal for a Differential Calculus in Quantum Mechanics

In this paper, using the Weyl-Wigner-Moyal formalism for quantum mechanics, we develop a {\it quantum-deformed} exterior calculus on the phase-space of an arbitrary hamiltonian system. Introducing additional bosonic and fermionic coordinates we construct a super-manifold which is closely related to the tangent and cotangent bundle over phase-space. Scalar functions on the super-manifold become equivalent to differential forms on the standard phase-space. The algebra of these functions is equipped with a Moyal super-star product which deforms the pointwise product of the classical tensor calculus. We use the Moyal bracket algebra in order to derive a set of quantum-deformed rules for the exterior derivative, Lie derivative, contraction, and similar operations of the Cartan calculus.Comment: TeX file with phyzzx macro, 43 pages, no figure

Bulges

We model the evolution of the galactic bulge and of the bulges of a selected sample of external spiral galaxies, via the multiphase multizone evolution model. We address a few questions concerning the role of the bulges within galactic evolution schemes and the properties of bulge stellar populations. We provide solutions to the problems of chemical abundances and spectral indices, the two main observational constraints to bulge structure.Comment: 15 pages, 10 figures, to be published in MNRA

The Negative Dimensional Oscillator at Finite Temperature

We study the thermal behavior of the negative dimensional harmonic oscillator of Dunne and Halliday that at zero temperature, due to a hidden BRST symmetry of the classical harmonic oscillator, is shown to be equivalent to the Grassmann oscillator of Finkelstein and Villasante. At finite temperature we verify that although being described by Grassmann numbers the thermal behavior of the negative dimensional oscillator is quite different from a Fermi system.Comment: 8 pages, IF/UFRJ/93/0

Non-Commutative Geometry, Multiscalars, and the Symbol Map

Starting from the concept of the universal exterior algebra in non-commutative differential geometry we construct differential forms on the quantum phase-space of an arbitrary system. They bear the same natural relationship to quantum dynamics which ordinary tensor fields have with respect to classical hamiltonian dynamics.Comment: 8 pages, late

On The Dynamic Programming Approach To Incentive Constraint Problems

In this paper we study a class of infinite horizon optimal control problems with incentive constraints in the discrete time case. More specifically, we establish suffcient conditions under which the value function associated to such problems satisfies the Dynamic Programming Principle.In this paper we study a class of infinite horizon optimal control problems with incentive constraints in the discrete time case. More specifically, we establish suffcient conditions under which the value function associated to such problems satisfies the Dynamic Programming Principle.Non-Refereed Working Papers / of national relevance onl

Neuroimaging Evidence of Major Morpho-Anatomical and Functional Abnormalities in the BTBR T+TF/J Mouse Model of Autism

BTBR T+tf/J (BTBR) mice display prominent behavioural deficits analogous to the defining symptoms of autism, a feature that has prompted a widespread use of the model in preclinical autism research. Because neuro-behavioural traits are described with respect to reference populations, multiple investigators have examined and described the behaviour of BTBR mice against that exhibited by C57BL/6J (B6), a mouse line characterised by high sociability and low self-grooming. In an attempt to probe the translational relevance of this comparison for autism research, we used Magnetic Resonance Imaging (MRI) to map in both strain multiple morpho-anatomical and functional neuroimaging readouts that have been extensively used in patient populations. Diffusion tensor tractography confirmed previous reports of callosal agenesis and lack of hippocampal commissure in BTBR mice, and revealed a concomitant rostro-caudal reorganisation of major cortical white matter bundles. Intact inter-hemispheric tracts were found in the anterior commissure, ventro-medial thalamus, and in a strain-specific white matter formation located above the third ventricle. BTBR also exhibited decreased fronto-cortical, occipital and thalamic gray matter volume and widespread reductions in cortical thickness with respect to control B6 mice. Foci of increased gray matter volume and thickness were observed in the medial prefrontal and insular cortex. Mapping of resting-state brain activity using cerebral blood volume weighted fMRI revealed reduced cortico-thalamic function together with foci of increased activity in the hypothalamus and dorsal hippocampus of BTBR mice. Collectively, our results show pronounced functional and structural abnormalities in the brain of BTBR mice with respect to control B6 mice. The large and widespread white and gray matter abnormalities observed do not appear to be representative of the neuroanatomical alterations typically observed in autistic patients. The presence of reduced fronto-cortical metabolism is of potential translational relevance, as this feature recapitulates previously-reported clinical observations

Is classical reality completely deterministic?

The concept of determinism for a classical system is interpreted as the requirement that the solution to the Cauchy problem for the equations of motion governing this system be unique. This requirement is generally assumed to hold for all autonomous classical systems. We give counterexamples of this view. Our analysis of classical electrodynamics in a world with one temporal and one spatial dimension shows that the solution to the Cauchy problem with the initial conditions of a particular type is not unique. Therefore, random behavior of closed classical systems is indeed possible. This finding provides a qualitative explanation of how classical strings can split. We propose a modified path integral formulation of classical mechanics to include indeterministic systems.Comment: Replace the paper with a revised versio

Stabilization of internal space in noncommutative multidimensional cosmology

We study the cosmological aspects of a noncommutative, multidimensional universe where the matter source is assumed to be a scalar field which does not commute with the internal scale factor. We show that such noncommutativity results in the internal dimensions being stabilizedComment: 8 pages, 1 figure, to appear in IJMP