Resolution of the strong CP problem

It is shown that the quark mass aligns QCD $\theta$ vacuum in such a way that the strong CP is conserved, resolving the strong CP problem.Comment: 9 pages;v2 slightly rewritten and expanded;v3 a few points clarified;v4 minor changes, journal versio

A Characterisation of the Weylian Structure of Space-Time by Means of Low Velocity Tests

The compatibility axiom in Ehlers, Pirani and Schild's (EPS) constructive axiomatics of the space-time geometry that uses light rays and freely falling particles with high velocity, is replaced by several constructions with low velocity particles only. For that purpose we describe in a space-time with a conformal structure and an arbitrary path structure the radial acceleration, a Coriolis acceleration and the zig-zag construction. Each of these quantities give effects whose requirement to vanish can be taken as alternative version of the compatibility axiom of EPS. The procedural advantage lies in the fact, that one can make null-experiments and that one only needs low velocity particles to test the compatibility axiom. We show in addition that Perlick's standard clock can exist in a Weyl space only.Comment: to appear in Gen.Rel.Gra

Field Decomposition and the Ground State Structure of SU(2) Yang-Mills Theory

We compute the effective potential of SU(2) Yang-Mills theory using the background field method and the Faddeev-Niemi decomposition of the gauge fields. In particular, we find that the potential will depend on the values of two scalar fields in the decomposition and that its structure will give rise to a symmetry breaking.Comment: 8 pages, 1 figure. Typos corrected and title change

Double Well Potential: Perturbation Theory, Tunneling, WKB (beyond instantons)

A simple approximate solution for the quantum-mechanical quartic oscillator $V= m^2 x^2+g x^4$ in the double-well regime $m^2<0$ at arbitrary $g \geq 0$ is presented. It is based on a combining of perturbation theory near true minima of the potential, semi-classical approximation at large distances and a description of tunneling under the barrier. It provides 9-10 significant digits in energies and gives for wavefunctions the relative deviation in real $x$-space less than $\lesssim 10^{-3}$.Comment: 13 pages, invited talk at "Crossing the boundaries: Gauge dynamics at strong coupling (Shifmania)", Minneapolis, May 14-17, 200

Universal Properties of Two-Dimensional Boson Droplets

We consider a system of N nonrelativistic bosons in two dimensions, interacting weakly via a short-range attractive potential. We show that for N large, but below some critical value, the properties of the N-boson bound state are universal. In particular, the ratio of the binding energies of (N+1)- and N-boson systems, B_{N+1}/B_N, approaches a finite limit, approximately 8.567, at large N. We also confirm previous results that the three-body system has exactly two bound states. We find for the ground state B_3^(0) = 16.522688(1) B_2 and for the excited state B_3^(1) = 1.2704091(1) B_2.Comment: 4 pages, 2 figures, final versio

The Theorem of Jentzsch--Szeg\H{o} on an analytic curve. Application to the irreducibility of truncations of power series

The theorem of Jentzsch--Szeg\H{o} describes the limit measure of a sequence of discrete measures associated to the zeroes of a sequence of polynomials in one variable. Following the presentation of this result by Andrievskii and Blatt in their book, we extend this theorem to compact Riemann surfaces, then to analytic curves over an ultrametric field. The particular case of the projective line over an ultrametric field gives as corollaries information about the irreducibility of the truncations of a power series in one variable.Comment: 16 pages; the application to irreducibility and the final example have been correcte

Comment on "Feynman Effective Classical Potential in the Schrodinger Formulation"

We comment on the paper "Feynman Effective Classical Potential in the Schrodinger Formulation"[Phys. Rev. Lett. 81, 3303 (1998)]. We show that the results in this paper about the time evolution of a wave packet in a double well potential can be properly explained by resorting to a variational principle for the effective action. A way to improve on these results is also discussed.Comment: 1 page, 2eps figures, Revte