Dirac's Footsteps and Supersymmetry

One hundred years after its creator's birth, the Dirac equation stands as the cornerstone of XXth Century physics. But it is much more, as it carries the seeds of supersymmetry. Dirac also invented the light-cone, or "front form" dynamics, which plays a crucial role in string theory and in elucidating the finiteness of N=4 Yang-Mills theory. The light-cone structure of eleven-dimensional supergravity (N=8 supergravity in four dimensions) suggests a group-theoretical interpretation of its divergences. We speculate they could be compensated by an infinite number of triplets of massless higher spin fields, each obeying a Dirac-like equation associated with the coset $F_4/SO(9)$. The divergences are proportional to the trace over a non-compact structure containing the compact form of $F_4$. Its nature is still unknown, but it could show the way to $M$-theory.Comment: Invited Talk at Dirac's Centennial Symposium, Tallahasse, Florida, Dec 200

Quintics with Finite Simple Symmetries

We construct all quintic invariants in five variables with simple Non-Abelian finite symmetry groups. These define Calabi-Yau three-folds which are left invariant by the action of A_5, A_6 or PSL_2(11).Comment: 18 pages, typos corrected, matches published versio

Gauge symmetry and Slavnov-Taylor identities for randomly stirred fluids

The path integral for randomly forced incompressible fluids is shown to have an underlying Becchi-Rouet-Stora (BRS) symmetry as a consequence of Galilean invariance. This symmetry must be respected to have a consistent generating functional, free from both an overall infinite factor and spurious relations amongst correlation functions. We present a procedure for respecting this BRS symmetry, akin to gauge fixing in quantum field theory. Relations are derived between correlation functions of this gauge fixed, BRS symmetric theory, analogous to the Slavnov-Taylor identities of quantum field theory.Comment: 5 pages, no figures, In Press Physical Review Letters, 200

Anti-shielding Effect and Negative Temperature in Instantaneously Reversed Electric Fields and Left-Handed Media

The connections between the anti-shielding effect, negative absolute temperature and superluminal light propagation in both the instantaneously reversed electric field and the left-handed media are considered in the present paper. The instantaneous inversion of the exterior electric field may cause the electric dipoles into the state of negative absolute temperature and therefore give rise to a negative effective mass term of electromagnetic field (i. e., the electromagnetic field propagating inside the negative-temperature medium will acquire an imaginary rest mass), which is said to result in the potential superluminality effect of light propagation in this anti-shielding dielectric. In left-handed media, such phenomena may also arise.Comment: 9 pages, Late

L'usage des systèmes d'informations électroniques en recherche scientifique : le cas de la neurophysiologie.

Nous présentons les premiers résultats d'une enquête destinée à mieux connaître les pratiques de recherche d'information bibliographique et documentaire chez les chercheurs scientifiques. 64 chercheurs et étudiants doctorants en neurophysiologie ont répondu à un questionnaire portant sur les méthodes, les outils, et les objectifs des recherches d'information typiques dans leur activité. De plus, 11 personnes parmi les répondants ont participé à un entretien individuel semi structuré. Il en ressort que l'usage d'outils informatisés de recherche d'information bibliographique (RIB) est désormais pratique courante, au détriment des index et autres sources imprimées. Les principaux outils utilisés sont la base de données bibliographiques PubMed et le moteur de recherche Google, avec toutefois de nombreux autres outils plus spécifiques utilisés à titre complémentaire. Les répondants mentionnent des objectifs très variés, comme l'acquisition de connaissances nouvelles, mais aussi la recherche de techniques expérimentales, la veille documentaire, l'alimentation du débat scientifique, ou l'aide à l'enseignement. Les difficultés que rencontrent les experts en neurosciences intégratives dans l'exploitation des outils informatiques de RIB spécialisés semblent surtout liées à l'absence de formation des experts à ces outils. Les chercheurs définissent l'outil informatique de RIB « idéal » comme fiable et exhaustif, mais aussi rapide et facile à utiliser et apprendre . De fait, le facteur temps apparaît déterminant dans leur choix d'utilisation ou non d'un outil particulier. Cette étude ouvre la voie à des expériences plus spécifiques, qui porteront sur les stratégies cognitives des experts dans ce type de tâches

The U(1)A anomaly in noncommutative SU(N) theories

We work out the one-loop $U(1)_A$ anomaly for noncommutative SU(N) gauge theories up to second order in the noncommutative parameter $\theta^{\mu\nu}$. We set $\theta^{0i}=0$ and conclude that there is no breaking of the classical $U(1)_A$ symmetry of the theory coming from the contributions that are either linear or quadratic in $\theta^{\mu\nu}$. Of course, the ordinary anomalous contributions will be still with us. We also show that the one-loop conservation of the nonsinglet currents holds at least up to second order in $\theta^{\mu\nu}$. We adapt our results to noncommutative gauge theories with SO(N) and U(1) gauge groups.Comment: 50 pages, 5 figures in eps files. Some comments and references adde

On the two-loop contributions to the pion mass

We derive a simplified representation for the pion mass to two loops in three-flavour chiral perturbation theory. For this purpose, we first determine the reduced expressions for the tensorial two-loop 2-point sunset integrals arising in chiral perturbation theory calculations. Making use of those relations, we obtain the expression for the pion mass in terms of the minimal set of master integrals. On the basis of known results for these, we arrive at an explicit analytic representation, up to the contribution from K-K-eta intermediate states where a closed-form expression for the corresponding sunset integral is missing. However, the expansion of this function for a small pion mass leads to a simple representation which yields a very accurate approximation of this contribution. Finally, we also give a discussion of the numerical implications of our results.Comment: Typos corrected and minor changes in Table 2. Published version. 19 pages, 1 figure, 2 table

Generating functional for the gravitational field: implementation of an evolutionary quantum dynamics

We provide a generating functional for the gravitational field, associated to the relaxation of the primary constraints as extended to the quantum sector. This requirement of the theory, relies on the assumption that a suitable time variable exist, when taking the T-products of the dynamical variables. More precisely, we start from the gravitational field equations written in the Hamiltonian formalism and expressed via Misner-like variables; hence we construct the equation to which the T-products of the dynamical variables obey and transform this paradigm in terms of the generating functional, as taken on the theory phase-space. We show how the relaxation of the primary constraints (which correspond to break down the invariance of the quantum theory under the 4-diffeomorphisms) is summarized by a free functional taken on the Lagrangian multipliers, accounting for such constraints in the classical theory. The issue of our analysis is equivalent to a Gupta-Bleuler approach on the quantum implementation of all the gravitational constraints; in fact, in the limit of small $\hbar$, the quantum dynamics is described by a Schr\"odinger equation, as soon as the mean values of the momenta, associated to the lapse function and the shift vector, are not vanishing. Finally we show how, in the classical limit, the evolutionary quantum gravity reduces to General Relativity in the presence of an Eckart fluid, which corresponds to the classical counterpart of the physical clock, introduced in the quantum theory.Comment: 23 pages, no figures, to appear on International Journal of Modern Physics

Raising the unification scale in supersymmetry

In the minimal supersymmetric standard model, the three gauge couplings appear to unify at a mass scale near $2 \times 10^{16}$ GeV. We investigate the possibility that intermediate scale particle thresholds modify the running couplings so as to increase the unification scale. By requiring consistency of this scenario, we derive some constraints on the particle content and locations of the intermediate thresholds. There are remarkably few acceptable solutions with a single cleanly defined intermediate scale far below the unification scale.Comment: 22 pages, macros included. One figure, available at ftp://ftp.phys.ufl.edu/incoming/rais.ep

Phase transition in the 3-D massive Gross-Neveu model

We consider the 3-dimensional massive Gross-Neveu model at finite temperature as an effective theory for strong interactions. Using the Matsubara imaginary time formalism, we derive a closed form for the renormalized $T$-dependent four-point function. This gives a singularity, suggesting a phase transition. Considering the free energy we obtain the $T$-dependent mass, which goes to zero for some temperature. These results lead us to the conclusion that there is a second-order phase transition.Comment: 06 pages, 02 figures, LATE