The planar spectrum in U(N)-invariant quantum mechanics by Fock space methods: I. The bosonic case

Prompted by recent results on Susy-U(N)-invariant quantum mechanics in the large N limit by Veneziano and Wosiek, we have examined the planar spectrum in the full Hilbert space of U(N)-invariant states built on the Fock vacuum by applying any U(N)-invariant combinations of creation-operators. We present results about 1) the supersymmetric model in the bosonic sector, 2) the standard quartic Hamiltonian. This latter is useful to check our techniques against the exact result of Brezin et al. The SuSy case is where Fock space methods prove to be the most efficient: it turns out that the problem is separable and the exact planar spectrum can be expressed in terms of the single-trace spectrum. In the case of the anharmonic oscillator, on the other hand, the Fock space analysis is quite cumbersome due to the presence of large off-diagonal O(N) terms coupling subspaces with different number of traces; these terms should be absorbed before taking the planar limit and recovering the known planar spectrum. We give analytical and numerical evidence that good qualitative information on the spectrum can be obtained this way.Comment: 17 pages, 4 figures, uses youngtab.sty. Final versio

Relationship between resistivity and specific heat in a canonical non-magnetic heavy fermion alloy system: UPt_5-xAu_x

UPt_(5-x)Au_x alloys form in a single crystal structure, cubic AuBe_5-type, over a wide range of concentrations from x = 0 to at least x = 2.5. All investigated alloys, with an exception for x = 2.5, were non-magnetic. Their electronic specific heat coefficient $\gamma$ varies from about 60 (x = 2) to about 700 mJ/mol K^2 (x = 1). The electrical resistivity for all alloys has a Fermi-liquid-like temperature variation, \rho = \rho_o + AT^2, in the limit of T -> 0 K. The coefficient A is strongly enhanced in the heavy-fermion regime in comparison with normal and transition metals. It changes from about 0.01 (x = 0) to over 2 micro-ohm cm/K^2 (x = 1). A/\gamma^2, which has been postulated to have a universal value for heavy-fermions, varies from about 10^-6 (x = 0, 0.5) to 10^-5 micro-ohm cm (mol K/mJ)^2 (x > 1.1), thus from a value typical of transition metals to that found for some other heavy-fermion metals. This ratio is unaffected, or only weakly affected, by chemical or crystallographic disorder. It correlates with the paramagnetic Curie-Weiss temperature of the high temperature magnetic susceptibility.Comment: 5 pages, 5 eps figures, RevTe

Hamiltonian Analysis of non-chiral Plebanski Theory and its Generalizations

We consider non-chiral, full Lorentz group-based Plebanski formulation of general relativity in its version that utilizes the Lagrange multiplier field Phi with "internal" indices. The Hamiltonian analysis of this version of the theory turns out to be simpler than in the previously considered in the literature version with Phi carrying spacetime indices. We then extend the Hamiltonian analysis to a more general class of theories whose action contains scalars invariants constructed from Phi. Such theories have recently been considered in the context of unification of gravity with other forces. We show that these more general theories have six additional propagating degrees of freedom as compared to general relativity, something that has not been appreciated in the literature treating them as being not much different from GR.Comment: 10 page

Plebanski Theory and Covariant Canonical Formulation

We establish an equivalence between the Hamiltonian formulation of the Plebanski action for general relativity and the covariant canonical formulation of the Hilbert-Palatini action. This is done by comparing the symplectic structures of the two theories through the computation of Dirac brackets. We also construct a shifted connection with simplified Dirac brackets, playing an important role in the covariant loop quantization program, in the Plebanski framework. Implications for spin foam models are also discussed.Comment: 18 page

Exact and semiclassical approach to a class of singular integral operators arising in fluid mechanics and quantum field theory

A class of singular integral operators, encompassing two physically relevant cases arising in perturbative QCD and in classical fluid dynamics, is presented and analyzed. It is shown that three special values of the parameters allow for an exact eigenfunction expansion; these can be associated to Riemannian symmetric spaces of rank one with positive, negative or vanishing curvature. For all other cases an accurate semiclassical approximation is derived, based on the identification of the operators with a peculiar Schroedinger-like operator.Comment: 12 pages, 1 figure, amslatex, bibtex (added missing label eq.11

Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity

We give an independent derivation of the Engle-Pereira-Rovelli spinfoam model for quantum gravity which recently appeared in [arXiv:0705.2388]. Using the coherent state techniques introduced earlier in [arXiv:0705.0674], we show that the EPR model realizes a consistent imposition of the simplicity constraints implementing general relativity from a topological BF theory.Comment: 6 pages, 2 figures, v2: typos correcte

Projected Spin Networks for Lorentz connection: Linking Spin Foams and Loop Gravity

In the search for a covariant formulation for Loop Quantum Gravity, spin foams have arised as the corresponding discrete space-time structure and, among the different models, the Barrett-Crane model seems the most promising. Here, we study its boundary states and introduce cylindrical functions on both the Lorentz connection and the time normal to the studied hypersurface. We call them projected cylindrical functions and we explain how they would naturally arise in a covariant formulation of Loop Quantum Gravity.Comment: Latex, 15 page

Revisiting the Simplicity Constraints and Coherent Intertwiners

In the context of loop quantum gravity and spinfoam models, the simplicity constraints are essential in that they allow to write general relativity as a constrained topological BF theory. In this work, we apply the recently developed U(N) framework for SU(2) intertwiners to the issue of imposing the simplicity constraints to spin network states. More particularly, we focus on solving them on individual intertwiners in the 4d Euclidean theory. We review the standard way of solving the simplicity constraints using coherent intertwiners and we explain how these fit within the U(N) framework. Then we show how these constraints can be written as a closed u(N) algebra and we propose a set of U(N) coherent states that solves all the simplicity constraints weakly for an arbitrary Immirzi parameter.Comment: 28 page

Local dark matter searches with LISA

The drag-free satellites of LISA will maintain the test masses in geodesic motion over many years with residual accelerations at unprecedented small levels and time delay interferometry (TDI) will keep track of their differential positions at level of picometers. This may allow investigations of fine details of the gravitational field in the Solar System previously inaccessible. In this spirit, we present the concept of a method to measure directly the gravitational effect of the density of diffuse Local Dark Matter (LDM) with a constellation of a few drag-free satellites, by exploiting how peculiarly it would affect their relative motion. Using as test bed an idealized LISA with rigid arms, we find that the separation in time between the test masses is uniquely perturbed by the LDM, so that they acquire a differential breathing mode. Such a LDM signal is related to the LDM density within the orbits and has characteristic spectral components, with amplitudes increasing in time, at various frequencies of the dynamics of the constellation. This is the relevant result, in that the LDM signal is brought to non-zero frequencies.Comment: 8 pages, 1 figure; v2: minor changes to match the version in press on Classical and Quantum Gravity (special issue for the 7th International LISA Symposium proceedings

Modulation of LISA free-fall orbits due to the Earth-Moon system

We calculate the effect of the Earth-Moon (EM) system on the free-fall motion of LISA test masses. We show that the periodic gravitational pulling of the EM system induces a resonance with fundamental frequency 1 yr^-1 and a series of periodic perturbations with frequencies equal to integer harmonics of the synodic month (9.92 10^-7 Hz). We then evaluate the effects of these perturbations (up to the 6th harmonics) on the relative motions between each test masses couple, finding that they range between 3mm and 10pm for the 2nd and 6th harmonic, respectively. If we take the LISA sensitivity curve, as extrapolated down to 10^-6 Hz, we obtain that a few harmonics of the EM system can be detected in the Doppler data collected by the LISA space mission. This suggests that the EM system gravitational near field could provide an absolute calibration for the LISA sensitivity at very low frequencies.Comment: 15 pages, 5 figure