New Application of Functional Integrals to Classical Mechanics

In this paper a new functional integral representation for classical dynamics is introduced. It is achieved by rewriting the Liouville picture in terms of bosonic creation-annihilation operators and utilizing the standard derivation of functional integrals for dynamical quantities in the coherent states representation. This results in a new class of functional integrals which are exactly solvable and can be found explicitly when the underlying classical systems are integrable.Comment: 13 page

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

Quantum properties of a cyclic structure based on tripolar fields

The properties of cyclic structures (toroidal oscillators) based on classical tripolar (colour) fields are discussed, in particular, of a cyclic structure formed of three colour-singlets spinning around a ring-closed axis. It is shown that the helicity and handedness of this structure can be related to the quantum properties of the electron. The symmetry of this structure corresponds to the complete cycle of ${2/3}\pi$-rotations of its constituents, which leads to the exact overlapping of the paths of its three complementary coloured constituents, making the system dynamically colourless. The gyromagnetic ratio of this system is estimated to be g$\approx 2$, which agrees with the Land\'e g-factor for the electron.Comment: 11 pages, 4 figures, journal versio

Gauge Interaction as Periodicity Modulation

The paper is devoted to a geometrical interpretation of gauge invariance in terms of the formalism of field theory in compact space-time dimensions [arXiv:0903.3680]. In this formalism, the kinematic information of an interacting elementary particle is encoded on the relativistic geometrodynamics of the boundary of the theory through local transformations of the underlying space-time coordinates. Therefore, gauge interaction is described as invariance of the theory under local deformations of the boundary, the resulting local variations of field solution are interpreted as internal transformations, and the internal symmetries of the gauge theory turn out to be related to corresponding local space-time symmetries. In the case of local infinitesimal isometric transformations, Maxwell's kinematics and gauge invariance are inferred directly from the variational principle. Furthermore we explicitly impose periodic conditions at the boundary of the theory as semi-classical quantization condition in order to investigate the quantum behavior of gauge interaction. In the abelian case the result is a remarkable formal correspondence with scalar QED.Comment: 37 pages, 2 figures. Version published in Annals of Physics (2012). New title, comments and minor correction

Non-commutative multi-dimensional cosmology

A non-commutative multi-dimensional cosmological model is introduced and used to address the issues of compactification and stabilization of extra dimensions and the cosmological constant problem. We show that in such a scenario these problems find natural solutions in a universe described by an increasing time parameter.Comment: 9 pages, 1 figure, to appear in JHE

Supersymmetry and Integrability in Planar Mechanical Systems

We present an N=2-supersymmetric mechanical system whose bosonic sector, with two degrees of freedom, stems from the reduction of an SU(2) Yang-Mills theory with the assumption of spatially homogeneous field configurations and a particular ansatz imposed on the gauge potentials in the dimensional reduction procedure. The Painleve test is adopted to discuss integrability and we focus on the role of supersymmetry and parity invariance in two space dimensions for the attainment of integrable or chaotic models. Our conclusion is that the relationships among the parameters imposed by supersymmetry seem to drastically reduce the number of possibilities for integrable interaction potentials of the mechanical system under consideration.Comment: 20 pages, 3 figure

Stochastic Quantization of Scalar Fields in Einstein and Rindler Spacetime

We consider the stochastic quantization method for scalar fields defined in a curved manifold and also in a flat space-time with event horizon. The two-point function associated to a massive self-interacting scalar field is evaluated, up to the first order level in the coupling constant, for the case of an Einstein and also a Rindler Euclidean metric, respectively. Its value for the asymptotic limit of the Markov parameter is exhibited. The divergences therein are taken care of by employing a covariant stochastic regularization

Mechanical similarity as a generalization of scale symmetry

In this paper we study the symmetry known as mechanical similarity (LMS) and present for any monomial potential. We analyze it in the framework of the Koopman-von Neumann formulation of classical mechanics and prove that in this framework the LMS can be given a canonical implementation. We also show that the LMS is a generalization of the scale symmetry which is present only for the inverse square potential. Finally we study the main obstructions which one encounters in implementing the LMS at the quantum mechanical level.Comment: 9 pages, Latex, a new section adde

Noncommutativity, generalized uncertainty principle and FRW cosmology

We consider the effects of noncommutativity and the generalized uncertainty principle on the FRW cosmology with a scalar field. We show that, the cosmological constant problem and removability of initial curvature singularity find natural solutions in this scenarios.Comment: 8 pages, to appear in IJT

Thermodynamic formalism for systems with Markov dynamics

The thermodynamic formalism allows one to access the chaotic properties of equilibrium and out-of-equilibrium systems, by deriving those from a dynamical partition function. The definition that has been given for this partition function within the framework of discrete time Markov chains was not suitable for continuous time Markov dynamics. Here we propose another interpretation of the definition that allows us to apply the thermodynamic formalism to continuous time. We also generalize the formalism --a dynamical Gibbs ensemble construction-- to a whole family of observables and their associated large deviation functions. This allows us to make the connection between the thermodynamic formalism and the observable involved in the much-studied fluctuation theorem. We illustrate our approach on various physical systems: random walks, exclusion processes, an Ising model and the contact process. In the latter cases, we identify a signature of the occurrence of dynamical phase transitions. We show that this signature can already be unravelled using the simplest dynamical ensemble one could define, based on the number of configuration changes a system has undergone over an asymptotically large time window.Comment: 64 pages, LaTeX; version accepted for publication in Journal of Statistical Physic