Classical and quantum aspects of the extended antifield formalism

Agrégation de l'enseignement supérieur, Orientation sciences

VegeDog: Formalism, vegetarian dogs, and partonomies in transition

The pragmatics of 'vegetarian' and 'carnivorous' exhibits an asymmetry that we put in evidence by analyzing a newspaper report about vegetarian dog-owners imposing a vegetarian diet on their pets. More fundamental is the problem of partonomy versus containment, for which we attempt a naive but formal analysis applied to ingestion and the food chain, an issue we derive from the same text analyzed. Our formal tools belong in commonsense modelling, a domain of artificial intelligence related to extra-linguistic knowledge and pragmatics. We first provide an interpretation of events analyzed, and express it graphically in a semantic-network related representation, and propose an alternative that we express in terms of a modal logic, avoiding the full representational power of Hayes's "ontology for liquids".

An AI formalism for competing claims of identification: capturing the "Smemorato di Collegno" amnesia case

A formal representation is given of the situational structure, and the agents' beliefs about personal identity, in the Smemorato di Collegno amnesia case tried in 1927, in Pollenza, Italy. Another section discusses and formalizes a sample heuristic rule for conjecturing whether an individual identity other than personal, being conveyed by a toponym, was used literally or fictitiously in a given historical corpus of legal casenotes. For example, a landlocked city being named and referred to as though it was a sea port is a fairly good cue for assuming that the toponym is a disguise. Yet, the interpretation is governed by other conventions, when in a play by Shakeaspeare it is stated that a given scene is set on the sea coast of Bohemia. Further discussion of a situational casuistry for identification (especially individual and personal) along with more formal representations will appear in a companion paper "nissanidentifpirandello", also at the disciplinary meet of AI formalisms and legal applications.

Correlated electron-ion dynamics with open boundaries: formalism

We extend a new formalism, which allows correlated electron-ion dynamics to be applied to the problem of open boundary conditions. We implement this at the first moment level (allowing heating of ions by electrons) and observe the expected cooling in the classical part of the ionic kinetic energy and current-induced heating in the quantum contribution. The formalism for open boundaries should be easily extended to higher moments of the correlated electron-ion fluctuations.

Temperature-dependent gap edge in strong-coupling superconductors determined using the Eliashberg-Nambu formalism

Using the theory of Eliashberg and Nambu for strong-coupling superconductors, we have calculated the gap function for a model superconductor and a selection of real superconductors includong the elements Al, Sn, Tl, Nb, In, Pb and Hg and one alloy, Bi2Tl. We have determined thetemperature-dependent gap edge in each and found that in materials with weak electron-phonon ($\lambda 1.20$), not only is the gap edge double valued but it also departs significantly from the BCS form and develops a shoulderlike structure which may, in some cases, denote a gap edge exceeding the $T = 0$ value. These computational results support the insights obtained by Leavens in an analytic consideration of the general problem. Both the shoulder and double value arise from a common origin seated in the form of the gap function in strong coupled materials at finite temperatures. From the calculated gap function, we can determine the densities of states in the materials and the form of the tunneling current-voltage characteristics for junctions with these materials as electroddes. By way of illustration, results are shown for the contrasting cases of Sn ($\lambda=0.74$) and Hg ($\lambad=1.63$). The reported results are distinct in several ways from BCS predictions and provide an incentive determinative experimental studies with techniques such as tunneling and far infrared absorption.

A multiconfigurational time-dependent Hartree-Fock method for excited electronic states. I. General formalism and application to open-shell states

The solution of the time-dependent Schrodinger equation for systems of interacting electrons is generally a prohibitive task, for which approximate methods are necessary. Popular approaches, such as the time-dependent Hartree-Fock (TDHF) approximation and time-dependent density functional theory (TDDFT), are essentially single-configurational schemes. TDHF is by construction incapable of fully accounting for the excited character of the electronic states involved in many physical processes of interest; TDDFT, although exact in principle, is limited by the currently available exchange-correlation functionals. On the other hand, multiconfigurational methods, such as the multiconfigurational time-dependent Hartree-Fock (MCTDHF) approach, provide an accurate description of the excited states and can be systematically improved. However, the computational cost becomes prohibitive as the number of degrees of freedom increases, and thus, at present, the MCTDHF method is only practical for few-electron systems. In this work, we propose an alternative approach which effectively establishes a compromise between efficiency and accuracy, by retaining the smallest possible number of configurations that catches the essential features of the electronic wavefunction. Based on a time-dependent variational principle, we derive the MCTDHF working equation for a multiconfigurational expansion with fixed coefficients and specialise to the case of general open-shell states, which are relevant for many physical processes of interest. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3600397]

Analysis of Fluctuations in the Early Universe Using Fokker-Planck Formalism

The thesis begins with a review of basic elements of general theory of relativity (GTR) which forms the basis for the theoretical interpretation of the observations in cosmology. The first chapter also discusses the standard model in cosmology, namely the Friedmann model, its predictions and problems. We have also made a brief discussion on fractals and inflation of the early universe in the first chapter. In the second chapter we discuss the formulation of a new approach to cosmology namely a stochastic approach. In this model, the dynam ics of the early universe is described by a set of non-deterministic, Langevin type equations and we derive the solutions using the Fokker—Planck formalism. Here we demonstrate how the problems with the standard model, can be eliminated by introducing the idea of stochastic fluctuations in the early universe. Many recent observations indicate that the present universe may be approximated by a many component fluid and we assume that only the total energy density is conserved. This, in turn, leads to energy transfer between different components of the cosmic fluid and fluctuations in such energy transfer can certainly induce fluctuations in the mean to factor in the equation of state p = wp, resulting in a fluctuating expansion rate for the universe. The third chapter discusses the stochastic evolution of the cosmological parameters in the early universe, using the new approach. The penultimate chapter is about the refinements to be made in the present model, by means of a new deterministic model The concluding chapter presents a discussion on other problems with the conventional cosmology, like fractal correlation of galactic distribution. The author attempts an explanation for this problem using the stochastic approach.

A new proposal for the picture changing operators in the minimal pure spinor formalism

Using a new proposal for the ""picture lowering"" operators, we compute the tree level scattering amplitude in the minimal pure spinor formalism by performing the integration over the pure spinor space as a multidimensional Cauchy-type integral. The amplitude will be written in terms of the projective pure spinor variables, which turns out to be useful to relate rigorously the minimal and non-minimal versions of the pure spinor formalism. The natural language for relating these formalisms is the. Cech-Dolbeault isomorphism. Moreover, the Dolbeault cocycle corresponding to the tree-level scattering amplitude must be evaluated in SO(10)/SU(5) instead of the whole pure spinor space, which means that the origin is removed from this space. Also, the. Cech-Dolbeault language plays a key role for proving the invariance of the scattering amplitude under BRST, Lorentz and supersymmetry transformations, as well as the decoupling of unphysical states. We also relate the Green`s function for the massless scalar field in ten dimensions to the tree-level scattering amplitude and comment about the scattering amplitude at higher orders. In contrast with the traditional picture lowering operators, with our new proposal the tree level scattering amplitude is independent of the constant spinors introduced to define them and the BRST exact terms decouple without integrating over these constant spinors.

GHP: a maple package for performing calculations in the Geroch-Held-Penrose formalism

We present a new symbolic algebra package, written for Maple, for performing computations in the Geroch-Held-Penrose formalism. We demonstrate the essential features and capabilities of our package by investigating Petrov-D vacuum solutions of Einstein's field equations.

A unified formalism for landmark based representation of maps and navigation plans

We present a unified formalism for representing maps and using them for constructing plans of navigation for an autonomous agent. The foundation of this work lies in addressing key questions that an agent is confronted with when navigating. That is, besides the main task of how to reach the intended destination from the current position, the agent faces other questions like: where am I? what landmarks can I see? where is my destination relative to me and the landmarks I am seeing? Fundamental to this representation is the use of visual landmarks, which are used as pivotal points in the landscape being described. Further, in the representation of spatial information and navigation there are three different viewpoints: first, the localized representation from the viewpoint of a sighted, mobile agent; second, the static representation seen by the map-maker; and third, the view of an external agent giving directions on the basis of his own experience/knowledge. The major contribution of this map model and the associated navigation method lies in the framework which unifies these three different points of view. This unification enables the agent to make no distinction in terms of following implicit instructions contained in a map and the directions given by external agents.