# SISSA Preprints

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This community holds the preprint created in SISSA and that are not peer-reviewed.

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Item Some classes of inverse spectral problems for quantum graphs(SISSA, 30-08-2016) Olivieri, Marco; Finco, D.; MathematicsInverse spectral problems for quantum graphs are analyzed. Under hypothesis of rational independence of lengths of edges it is possible, thanks to trace formulas, to reconstruct every information of compact and not compact graphs from the knowledge, respectively, of the spectrum of Laplacian and of the scattering phase. In the case of Sturm-Liouville operators defined on the graphs and more in general for differential operators, unknown potentials can be recovered from the knowledge of the spectrum of operators.Item About quantization of gravity(SISSA Library, 1984) Furlan, Giuseppe; de Alfaro, Vittorio; Fubini, Sergio; Physics; Elementary Particle TheoryItem Differential geometry of moduli spaces and its applications to soliton equations and to topological conformal field theory(Scuola Normale Superiore di Pisa, 1991-11) Dubrovin, Boris; MathematicsWe construct flat Riemannian metrics on moduli spaces of algebraic curves with marked meromorphic function. This gives a new class of exact algebraic-geometry solutions to certain non-linear equations in terms of functions on the moduli spaces. We show that the Riemannian metrics on the moduli spaces coincide with two-point correlators in topological conformal field theory and calculate the partition function for A_n model for arbitrary genus. A universal method for constructing complete families of conservation laws for Whitham-type hierarchies of PDEs is also proposed.Item Canonical and pertubative quantum gravity(1993) Esposito, Giampiero; physicsAfter a review of Dirac's theory of iconstrained Hamiltonian systems and their quantization, canonical quantum gravity is studied relying on the Arnowitt-Deser-Misner formalism. First-class constraints of the theory are studied in some detail following De Witt's work, and geometrical and topological properties of Wheeler's superspace are dis cussed following the mathematical work of Fisher. Perturbative quantum gravity is then formulated in terms of amplitudes of going from a three-metric and a matter-field configuration on a spacelike surface ~ to a three-metric and a field configuration on a spacelike surface ~'. The Wick-rotated quantum amplitudes are here studied under the assumption that the analytic continuation to the real Rieman- I nian section of the complexified space-time is possible, but this is not a generic property. Within the background-field method, one then expands both the four-metric g and mat ter fieldsItem Liouville and Toda field theories on Riemann surfaces(1993-03-10) Aldrovandi, E.; Bonora, L.; physicsWe study the Liouville theory on a Riemann surface of genus g by means of their associated Drinfeld–Sokolov linear systems. We discuss the cohomolog ical properties of the monodromies of these systems. We identify the space of solutions of the equations of motion which are single–valued and local and explic itly represent them in terms of Krichever–Novikov oscillators. Then we discuss the operator structure of the quantum theory, in particular we determine the quantum exchange algebras and find the quantum conditions for univalence and locality. We show that we can extend the above discussion to sl n Toda theoriesItem Algebraic structure of Lorentz and diffeomorphism anomalies(1993-04-03) Werneck de Oliveira, M.; Sorella, S.P.; physicsThe Wess-Zumino consistency conditions for Lorentz and diffeomor phism anomalies are discussed by introducing an operator δ whichallows to decompose the exterior space-time derivative as a BRS com mutator.Item Functional change of variables in the Wheeler-De Witt equation(SISSA, 1993-04-30) Cavaglià, Marco; Physics; AstrophysicsI present a new way to solve the Wheeler-de Witt equation using the invariance of the classical lagrangian under reparametrization. This property allows one to introduce an arbitrary function for each degree of freedom of the wave function $\Psi$: this arbitrariness can be used to fix the asymptotic behaviour of $\Psi$ so as to obtain a wave function representing a closed universe or a wormhole. These considerations are applied in detail to the Kantowsky-Sachs spacetime.Item Subdivision Analysis of Topological $Z_{p}$ Lattice Gauge Theory(SISSA, 1993-06-25) Birmingham, Danny; Rakowski, Mark; Physics; Elementary Particle TheoryWe analyze the subdivision properties of certain lattice gauge theories for the discrete abelian groups $Z_{p}$, in four dimensions. In these particular models we show that the Boltzmann weights are invariant under all $(k,l)$ subdivision moves, when the coupling scale is a $p$th root of unity. For the case of manifolds with boundary, we demonstrate analytically that Alexander type $2$ and $3$ subdivision of a bounding simplex is equivalent to the insertion of an operator which equals a delta function on trivial bounding holonomies. The four dimensional model then gives rise to an effective gauge invariant three dimensional model on its boundary, and we compute the combinatorially invariant value of the partition function for the case of $S^{3}$ and $S^{2}\times S^{1}$.Item The effective potential for the conformal factor in the standard model and beyond(SISSA, 1993-08-07) Percacci, Roberto; Physics; Elementary Particle TheoryThere is a general mechanism by which certain matter fields coupled to gravity can generate a nontrivial effective potential for the conformal factor of the metric. It is based on a nonstandard regularization method, with the cutoff being defined independently of the conformal factor. This mechanism produces a coupling of the matter fields to a dilaton, and a complicated interaction between matter, dilaton and metric. When it is applied to the standard model, it gives an effective potential which can be used to predict the top and Higgs masses. If the purely gravitational contribution to the potential is added, the mass of the dilaton is of the order of Planck's mass and the large hierarchy between the Planck and Fermi scales appears to be due to the smallness of the Higgs-dilaton coupling.Item A Unique Mass Function from Galaxies to Clusters ?(SISSA, 1993-08-11) Giuricin, Giuliano; Mardirossian, Fabio; Mezzetti, Marino; Persic, Massimo; Salucci, Paolo; Physics; AstrophysicsWe present an observational mass function ranging from galaxies to massive galaxy clusters, derived from direct dynamical mass estimates. Our mass function shows, in the low-mass range of galaxies and groups, a behaviour in agreement with that of standard CDM (n=-2), while in the high-mass range (clusters) our mass function is shallower (and thus contains more power) than standard CDM; it also results shallower than the recent mass function by Bahcall & Cen (1993, ApJ 407, L49).Item Towards the Classification of Exactly Solvable Feynman Path Integrals: $δ$-Function Perturbations and Boundary-Problems as Miscellaneous Solvable Models(SISSA, 1993-08-17) Grosche, Christian; Mathematics; Mathematical PhysicsIn this contribution I present further results on steps towards a Table of Feynman Path Integrals. Whereas the usual path integral solutions of the harmonic oscillator (Gaussian path integrals), of the radial harmonic oscillator (Besselian path integrals), and the (modified) P\"oschl-Teller potential(s) (Legendrian path integrals) are well known and can be performed explicitly by exploiting the convolution properties of the various types, a perturbative method opens other possibilities for calculating path integrals. Here I want to demonstrate the perturbation expansion method for point interactions and boundary problems in path integrals.Item Leptonic Decay Constants of Charm and Beauty Mesons in QCD: An Update(SISSA, 1993-09-14) Dominguez, C. A.; Physics; Elementary Particle TheoryAn update is given of the determination of leptonic decay constants of charm and beauty mesons in the framework of relativistic Hilbert moments and Laplace transform QCD sum rules.Item Correlation functions of two-matrix models(SISSA, 1993-11-16) Bonora, Loriano; Xiong, C. S.; Physics; Elementary Particle TheoryWe show how to calculate correlation functions of two matrix models. Our method consists in making full use of the integrable hierarchies and their reductions, which were shown in previous papers to naturally appear in multi-matrix models. The second ingredient we use are the $W$-constraints. In fact an explicit solution of the relevant hierarchy, satisfying the $W$-constraints (string equation), underlies the explicit calculation of the correlation functions. In the course of our derivation we do not use any continuum limit technique. This allows us to find many solutions which are invisible to the latter technique.Item Algebraic-geometrical Darboux coordinates in R-matrix formalism(SISSA, 1994) Diener, Paola; Dubrovin, Boris; Mathematics; Mathematical PhysicsItem Recurrent procedure for the determination of the free energy ε^2 expansion in the topological string theory(SISSA, 1999-03-30) Dubrovin, Boris; Maltsev, Andrei Ya A; MathematicsWe present here the iteration procedure for the determination of free energy ǫ2-expansion using the theory of KdV - type equations. In our approach we use the conservation laws for KdV - type equations depending explicitly on times t1, t2, . . . to find the ǫ2-expansion of u(x, t1, t2, . . .) after the infinite number of shifts of u(x, 0, 0, . . .) ≡ x along t1, t2, . . . in recurrent form. The formulas for the free energy expansion are just obtained then as a result of quite simple integration procedure applied to un(x).Item Topics in String Field Theory(SISSA, 2003) Bonora, Loriano; Maccaferri, Carlo; Mamone, Davide; Salizzoni, Mario; Physics; Elementary Particle TheoryThis review of bosonic string field theory is concentrated on two main subjects. In the first part we revisit the construction of the three string vertex and rederive the relevant Neumann coefficients both for the matter and the ghost part following a conformal field theory approach. We use this formulation to solve the VSFT equation of motion for the ghost sector. This part of the paper is based on a new method which allows us to derive known results in a simpler way. In the second part we concentrate on the solution of the VSFT equation of motion for the matter part. We describe the construction of the three strings vertex in the presence of a background B field. We determine a large family of lump solutions, illustrate their interpretation as D-branes and study the low energy limit. We show that in this limit the lump solutions flow toward the so-called GMS solitons.Item On non-perturbative extensions of anti-de-Sitter algebras(SISSA, 2003) Meessen, Patrick; Peeters, Kasper; Zamaklar, Marija; Physics; Elementary Particle TheoryMotivated by the study of branes in curved backgrounds, we investigate the construction of non-perturbative extensions of the super-isometry algebra osp*(8|4) of the AdS_7xS^4 background of M-theory. This algebra is not a subalgebra of osp(1|32) and its non-perturbative extension can therefore not be obtained by embedding in this simple superalgebra. We show how, instead, it is possible to construct an extension directly by solving the Jacobi identities. This requires, in addition to the expected non-perturbative charges, the introduction of new charges which appear in the {Q,Q} bracket only via a linear combination with the bosonic generators of the isometry algebra. The resulting extended algebra has the correct flat-space limit, but it is not simple and the non-perturbative charges do not commute with the super-isometry generators. We comment on the consequences of this structure for the representation theory and on possible alternatives to our construction.Item Prospects of probing $\theta_{13}$ and neutrino mass hierarchy by Supernova Neutrinos in KamLAND(SISSA, 2003) Bandyopadhyay, Abhijit; Choubey, Sandhya; Goswami, Srubabati; Kar, Kamales; Physics; Elementary Particle TheoryIn this paper we study the physics potential of the KamLAND detector in probing neutrino oscillation parameters through observation of supernova neutrinos. In particular, we discuss the possibilities of probing the mixing angle $\theta_{13}$ and determining the sign of $\Delta m^2_{32}$ from the total charged current(CC) event rates on the proton and $^{12}{C}$ target, as well as from the CC spectra. We discuss the chances of probing the earth matter effect induced modulations from the observation of CC spectra in the different CC reactions in KamLAND and find the volume required to get a statistically significant signature of the earth matter effect in different energy bins. We also calculate the event rates expected in the neutral current (NC) reactions on Carbon and free proton and investigate if the charged current to neutral current ratios, which are free of the absolute luminosity uncertainty in the supernova neutrino fluxes, can be useful in probing the oscillation parameters.Item Poisson Pencils, Integrability, and Separation of Variables(SISSA, 2003) Falqui, Gregorio; Mathematics; Mathematical PhysicsIn this paper we will review a recently introduced method for solving the Hamilton-Jacobi equations by the method of Separation of Variables. This method is based on the notion of pencil of Poisson brackets and on the bihamiltonian approach to integrable systems. We will discuss how separability conditions can be intrinsically characterized within such a geometrical set-up, the definition of the separation coordinates being encompassed in the \bih structure itself. We finally discuss these constructions studying in details a particular example, based on a generalization of the classical Toda Lattice.Item Quasi-periodic solutions of the equation v_{tt}-v_{xx}+v^3=f(v)(2005) Baldi, Pietro; Mathematics; Functional Analysis and ApplicationsWe consider 1D completely resonant nonlinear wave equations of the type vtt -vxx = -v 3 +O(v 4) with spatial periodic boundary conditions. We prove the existence of a new type of quasi-periodic small amplitude solutions with two frequencies, for more general nonlinearities. These solutions turn out to be, at the first order, the superposition of a traveling wave and a modulation of long period, depending only on time.