Positivity violation for the lattice Landau gluon propagator

We present explicit numerical evidence of reflection-positivity violation for the lattice Landau gluon propagator in three-dimensional pure SU(2) gauge theory. We use data obtained at very large lattice volumes (V = 80^3, 140^3) and for three different lattice couplings in the scaling region (beta = 4.2, 5.0, 6.0). In particular, we observe a clear oscillatory pattern in the real-space propagator C(t). We also verify that the (real-space) data show good scaling in the range t \in [0,3] fm and can be fitted using a Gribov-like form. The violation of positivity is in contradiction with a stable-particle interpretation of the associated field theory and may be viewed as a manifestation of confinement.Comment: 5 pages, 6 figures; minor modifications in the text and in the bibliograph

Negative-Energy Spinors and the Fock Space of Lattice Fermions at Finite Chemical Potential

Recently it was suggested that the problem of species doubling with Kogut-Susskind lattice fermions entails, at finite chemical potential, a confusion of particles with antiparticles. What happens instead is that the familiar correspondence of positive-energy spinors to particles, and of negative-energy spinors to antiparticles, ceases to hold for the Kogut-Susskind time derivative. To show this we highlight the role of the spinorial ``energy'' in the Osterwalder-Schrader reconstruction of the Fock space of non-interacting lattice fermions at zero temperature and nonzero chemical potential. We consider Kogut-Susskind fermions and, for comparison, fermions with an asymmetric one-step time derivative.Comment: 14p

Deceleration of neutral molecules in macroscopic traveling traps

A new type of decelerator is presented where polar neutral molecules are guided and decelerated using the principle of traveling electric potential wells, such that molecules are confined in stable three-dimensional traps throughout. This new decelerator is superior to the best currently operational decelerator (Scharfenberg et al., Phys.Rev.A 79, 023410(2009)), providing a substantially larger acceptance even at higher accelerations. The mode of operation is described and experimentally demonstrated by guiding and decelerating CO molecules.Comment: 10 pages, 3 figure

Continuum Limit of 2D2D Spin Models with Continuous Symmetry and Conformal Quantum Field Theory

According to the standard classification of Conformal Quantum Field Theory (CQFT) in two dimensions, the massless continuum limit of the $O(2)$ model at the Kosterlitz-Thouless (KT) transition point should be given by the massless free scalar field; in particular the Noether current of the model should be proportional to (the dual of) the gradient of the massless free scalar field, reflecting a symmetry enhanced from $O(2)$ to $O(2)\times O(2)$. More generally, the massless continuum limit of a spin model with a symmetry given by a Lie group $G$ should have an enhanced symmetry $G\times G$. We point out that the arguments leading to this conclusion contain two serious gaps: i) the possibility of `nontrivial local cohomology' and ii) the possibility that the current is an ultralocal field. For the $2D$ $O(2)$ model we give analytic arguments which rule out the first possibility and use numerical methods to dispose of the second one. We conclude that the standard CQFT predictions appear to be borne out in the $O(2)$ model, but give an example where they would fail. We also point out that all our arguments apply equally well to any $G$ symmetric spin model, provided it has a critical point at a finite temperature.Comment: 19 page

A traveling wave decelerator for neutral polar molecules

Recently, a decelerator for neutral polar molecules has been presented that operates on the basis of macroscopic, three-dimensional, traveling electrostatic traps (Osterwalder et al., Phys. Rev. A 81, 051401 (2010)). In the present paper, a complete description of this decelerator is given, with emphasis on the electronics and the mechanical design. Experimental results showing the transverse velocity distributions of guided molecules are shown and compared to trajectory simulations. An assessment of non-adiabatic losses is made by comparing the deceleration signals from 13-CO with those from 12-CO and with simulated signals.Comment: 10 pages, 7 figure

Algebraic Quantum Theory on Manifolds: A Haag-Kastler Setting for Quantum Geometry

Motivated by the invariance of current representations of quantum gravity under diffeomorphisms much more general than isometries, the Haag-Kastler setting is extended to manifolds without metric background structure. First, the causal structure on a differentiable manifold M of arbitrary dimension (d+1>2) can be defined in purely topological terms, via cones (C-causality). Then, the general structure of a net of C*-algebras on a manifold M and its causal properties required for an algebraic quantum field theory can be described as an extension of the Haag-Kastler axiomatic framework. An important application is given with quantum geometry on a spatial slice within the causally exterior region of a topological horizon H, resulting in a net of Weyl algebras for states with an infinite number of intersection points of edges and transversal (d-1)-faces within any neighbourhood of the spatial boundary S^2.Comment: 15 pages, Latex; v2: several corrections, in particular in def. 1 and in sec.

Connes-Lott model building on the two-sphere

In this work we examine generalized Connes-Lott models on the two-sphere. The Hilbert space of the continuum spectral triple is taken as the space of sections of a twisted spinor bundle, allowing for nontrivial topological structure (magnetic monopoles). The finitely generated projective module over the full algebra is also taken as topologically non-trivial, which is possible over $S^2$. We also construct a real spectral triple enlarging this Hilbert space to include "particle" and "anti-particle" fields.Comment: 57 pages, LATE

Functional Integral Construction of the Thirring model: axioms verification and massless limit

We construct a QFT for the Thirring model for any value of the mass in a functional integral approach, by proving that a set of Grassmann integrals converges, as the cutoffs are removed and for a proper choice of the bare parameters, to a set of Schwinger functions verifying the Osterwalder-Schrader axioms. The corresponding Ward Identities have anomalies which are not linear in the coupling and which violate the anomaly non-renormalization property. Additional anomalies are present in the closed equation for the interacting propagator, obtained by combining a Schwinger-Dyson equation with Ward Identities.Comment: 55 pages, 9 figure