Normal Coordinates and Primitive Elements in the Hopf Algebra of Renormalization

We introduce normal coordinates on the infinite dimensional group $G$ introduced by Connes and Kreimer in their analysis of the Hopf algebra of rooted trees. We study the primitive elements of the algebra and show that they are generated by a simple application of the inverse Poincar\'e lemma, given a closed left invariant 1-form on $G$. For the special case of the ladder primitives, we find a second description that relates them to the Hopf algebra of functionals on power series with the usual product. Either approach shows that the ladder primitives are given by the Schur polynomials. The relevance of the lower central series of the dual Lie algebra in the process of renormalization is also discussed, leading to a natural concept of $k$-primitiveness, which is shown to be equivalent to the one already in the literature.Comment: Latex, 24 pages. Submitted to Commun. Math. Phy

Real sector of the nonminimally coupled scalar field to self-dual gravity

A scalar field nonminimally coupled to gravity is studied in the canonical framework, using self-dual variables. The corresponding constraints are first class and polynomial. To identify the real sector of the theory, reality conditions are implemented as second class constraints, leading to three real configurational degrees of freedom per space point. Nevertheless, this realization makes non-polynomial some of the constraints. The original complex symplectic structure reduces to the expected real one, by using the appropriate Dirac brackets. For the sake of preserving the simplicity of the constraints, an alternative method preventing the use of Dirac brackets, is discussed. It consists of converting all second class constraints into first class by adding extra variables. This strategy is implemented for the pure gravity case.Comment: Latex file, 22 pages, no figure

Hopf Algebra Primitives in Perturbation Quantum Field Theory

The analysis of the combinatorics resulting from the perturbative expansion of the transition amplitude in quantum field theories, and the relation of this expansion to the Hausdorff series leads naturally to consider an infinite dimensional Lie subalgebra and the corresponding enveloping Hopf algebra, to which the elements of this series are associated. We show that in the context of these structures the power sum symmetric functionals of the perturbative expansion are Hopf primitives and that they are given by linear combinations of Hall polynomials, or diagrammatically by Hall trees. We show that each Hall tree corresponds to sums of Feynman diagrams each with the same number of vertices, external legs and loops. In addition, since the Lie subalgebra admits a derivation endomorphism, we also show that with respect to it these primitives are cyclic vectors generated by the free propagator, and thus provide a recursion relation by means of which the (n+1)-vertex connected Green functions can be derived systematically from the n-vertex ones.Comment: 21 pages, accepted for publication in J.Geom.and Phy

Revealing puddles of electrons and holes in compensated topological insulators

Three-dimensional topological insulators harbour metallic surface states with exotic properties. In transport or optics, these properties are typically masked by defect-induced bulk carriers. Compensation of donors and acceptors reduces the carrier density, but the bulk resistivity remains disappointingly small. We show that measurements of the optical conductivity in BiSbTeSe$_2$ pinpoint the presence of electron-hole puddles in the bulk at low temperatures, which is essential for understanding DC bulk transport. The puddles arise from large fluctuations of the Coulomb potential of donors and acceptors, even in the case of full compensation. Surprisingly, the number of carriers appearing within puddles drops rapidly with increasing temperature and almost vanishes around 40 K. Monte Carlo simulations show that a highly non-linear screening effect arising from thermally activated carriers destroys the puddles at a temperature scale set by the Coulomb interaction between neighbouring dopants, explaining the experimental observation semi-quantitatively. This mechanism remains valid if donors and acceptors do not compensate perfectly.Comment: 11 pages with 7 figures plus supplemental material (3 pages

Glow discharge mixture of Ar/He

Glow discharge mixture of Ar/He at a pressure of 266.66 Pa is experimentally investigated by opticalemission spectroscopy and double Langmuir probe at various mixture compositions. The species observedwere He I and Ar I. The electron temperature was found to be less than 10 eV, and the ion densityin the order of 1010 cm-3

BRST-BFV method for nonstationary systems

Starting from an associated reparametrization-invariant action, the generalization of the BRST-BFV method for the case of nonstationary systems is constructed. The extension of the Batalin-Tyutin conversional approach is also considered in the nonstationary case. In order to illustrate these ideas, the propagator for the time-dependent two-dimensional rotor is calculated by reformulating the problem as a system with only first class constraints and subsequently using the BRST-BFV prescription previously obtained.Comment: Latex, RevTeX, 13 page

Cuerpo y disciplina, orden y poder: Del Instructor Popular a los Tribunales Infantiles

A fines del siglo XIX, en la República Argentina, el periódico mendocino El Instructor Popular publica el intercambio epistolar entre dos graduados de la Escuela Normal de Paraná: Carlos Norberto Vergara y Ernesto A.Bavio. Reprender, reformar y corregir el error, las faltas y la ignorancia, fueron las justificaciones para hacer uso de punteros y palmetas e incorporar la pena, el dolor y la culpa como correctivos, en las instituciones educativas de "la letra con la sangre entra" en manos de "maestros normales que quieren gobernar con el lático". El espistolario visibiliza y reprueba ciertas prácticas que tuvieron al cuerpo infantil como territorio de anclaje para la institucionalización educativa. Puntear esa conjetura nos permite trazar continuidades y discontinuidades entre los "principios de la disciplina" y "los castigos corporales" como antecedentes para los "tribunales infantiles", implementados en la Escuela Quintana de la Provincia de Mendoza, por Florencia Fossatti, en las primeras décadas del siglo XX.Fil: Alvarado, Mariana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza. Instituto de Ciencias Humanas, Sociales y Ambientales; Argentin