arXiv subjects

P. A. Marchetti

Publications and source records attributed to P. A. Marchetti.

40 records · Page 3Linked to original sources

arXiv1995

Bosonization and Duality in Condensed Matter Systems

We show that abelian bosonization of 1+1 dimensional fermion systems can be interpreted as duality transformation and, as a conseguence, it can be generalized to arbitrary dimensions in terms of gauge forms of rank $d-1$, where $d$ is the dimension of the space. This permit to treat condensed matter systems in $d>1$ as gauge theories. Furthermore we show that in the ``scaling" limit the bosonized action is quadratic in a wide class of condensed matter systems. (Talk given at ``Common trends in Condensed Matter and High Energy Physics", September 3--10, 1995 -- Chia).

hep-th↗

arXiv1995

Algebraic-geometrical formulation of two-dimensional quantum gravity

We find a volume form on moduli space of double punctured Riemann surfaces whose integral satisfies the Painlevé I recursion relations of the genus expansion of the specific heat of 2D gravity. This allows us to express the asymptotic expansion of the specific heat as an integral on an infinite dimensional moduli space in the spirit of Friedan-Shenker approach. We outline a conjectural derivation of such recursion relations using the Duistermaat-Heckman theorem.

hep-th↗

arXiv1994

Nonperturbative 2D Gravity, Punctured Spheres and $Θ$-Vacua in String Theories

We consider a model of 2D gravity with the coefficient of the Einstein-Hilbert action having an imaginary part $π/2$. This is equivalent to introduce a $Θ$-vacuum structure in the genus expansion whose effect is to convert the expansion into a series of alternating signs, presumably Borel summable. We show that the specific heat of the model has a physical behaviour. It can be represented nonperturbatively as a series in terms of integrals over moduli spaces of punctured spheres and the sum of the series can be rewritten as a unique integral over a suitable moduli space of infinitely punctured spheres. This is an explicit realization à la Friedan-Shenker of 2D quantum gravity. We conjecture that the expansion in terms of punctures and the genus expansion can be derived using the Duistermaat-Heckman theorem. We briefly analyze expansions in terms of punctured spheres also for multicritical models.

hep-th↗

arXiv1994

Bosonization of Fermi Systems in Arbitrary Dimension in Terms of Gauge Forms

We present a general method to bosonize systems of Fermions with infinitely many degrees of freedom, in particular systems of non-relativistic electrons at positive density, by expressing the quantized conserved electric charge- and current density in terms of a bosonic antisymmetric tensorfield of a rank d--1, where d is the dimension of space. This enables us to make concepts and tools from gauge theory available for the purpose of analyzing electronic structure of non-relativistic matter. We apply our bosonization identities and concepts from gauge theory, such as Wegner -'t Hooft duality, to a variety of systems of condensed matter physics: Landau-Fermi liquids, Hall fluids, London superconductors, etc.. Among our results are an exact formula for the plasmon gap in a metal, a simple derivation of the Anderson-Higgs mechanism in superconductors, and an analysis of the orthogonality catastrophe for static sources.

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