Structure function of a damped harmonic oscillator

Following the Caldeira-Leggett approach to describe dissipative quantum systems the structure function for a harmonic oscillator with Ohmic dissipation is evaluated by an analytic continuation from euclidean to real time. The analytic properties of the Fourier transform of the structure function with respect to the energy transfer (the ``characteristic function'') are studied and utilized. In the one-parameter model of Ohmic dissipation we show explicitly that the broadening of excited states increases with the state number without violating sum rules. Analytic and numerical results suggest that this is a phenomenologically relevant, consistent model to include the coupling of a single (sub-)nuclear particle to unobserved and complex degrees of freedom.Comment: 23 pages, 5 figures, RevTex4, minor changes following referee's comments and by PRC: the definite article in the original title has been droppe

Exact Path-Integral Representations for the TT-Matrix in Nonrelativistic Potential Scattering

Several path integral representations for the $T$-matrix in nonrelativistic potential scattering are given which produce the complete Born series when expanded to all orders and the eikonal approximation if the quantum fluctuations are suppressed. They are obtained with the help of "phantom" degrees of freedom which take away explicit phases that diverge for asymptotic times. Energy conservation is enforced by imposing a Faddeev-Popov-like constraint in the velocity path integral. An attempt is made to evaluate stochastically the real-time path integral for potential scattering and generalizations to relativistic scattering are discussed.Comment: 6 pages, 2 figures. Contribution to the workshop "Relativistic Description of Two- and Three-Body Systems in Nuclear Physics", ETC*, October 19-23, 2009. v2: typo corrected, matches published version + additional reference

Polaron Variational Methods In The Particle Representation Of Field Theory : II. Numerical Results For The Propagator

For the scalar Wick-Cutkosky model in the particle representation we perform a similar variational calculation for the 2-point function as was done by Feynman for the polaron problem. We employ a quadratic nonlocal trial action with a retardation function for which several ans\"atze are used. The variational parameters are determined by minimizing the variational function and in the most general case the nonlinear variational equations are solved numerically. We obtain the residue at the pole, study analytically and numerically the instability of the model at larger coupling constants and calculate the width of the dressed particle.Comment: 25 pages standard LaTeX, 9 uuencoded postscript figures embedded with psfig.st

Updated dispersion-theoretical analysis of the nucleon electromagnetic form factors

In the light of the new data on the various neutron and proton electromagnetic form factors taken in recent years, we update the dispersion-theoretical analysis of the nucleon electromagnetic form factors from the mid-nineties. The parametrization of the spectral functions includes constraints from unitarity, perturbative QCD, and recent measurements of the neutron charge radius. We obtain a good description of most modern form factor data, with the exception of the Jefferson Lab data on G_E^p/G_M^p in the four-momentum transfer range Q^2=3...6 GeV^2. For the magnetic radii of the proton and the neutron we find r_M^p = 0.857 fm and r_M^n = 0.879 fm, which is consistent with the recent determinations using continued fraction expansions.Comment: 5 pages, 3 ps figures, final version, exp. errors in Figs. 1 and 3 correcte

Non-Perturbative Mass Renormalization in Quenched QED from the Worldline Variational Approach

Following Feynman's successful treatment of the polaron problem we apply the same variational principle to quenched QED in the worldline formulation. New features arise from the description of fermions by Grassmann trajectories, the supersymmetry between bosonic and fermionic variables and the much more singular structure of a renormalizable gauge theory like QED in 3+1 dimensions. We take as trial action a general retarded quadratic action both for the bosonic and fermionic degrees of freedom and derive the variational equations for the corresponding retardation functions. We find a simple analytic, non-perturbative, solution for the anomalous mass dimension gamma_m(alpha) in the MS scheme. For small couplings we compare our result with recent four-loop perturbative calculations while at large couplings we find that gamma_m(alpha) becomes proportional to (alpha)^(1/2). The anomalous mass dimension shows no obvious sign of the chiral symmetry breaking observed in calculations based on the use of Dyson-Schwinger equations, however we find that a perturbative expansion of gamma_m(alpha) diverges for alpha > 0.7934. Finally, we investigate the behaviour of gamma_m(alpha) at large orders in perturbation theory.Comment: 18 pages, 1 Figure, RevTeX; the manuscript has been substantially revised and enlarged in order to make it selfcontained; accepted for publication in Phys. Rev.

Variational Worldline Approximation for the Relativistic Two-Body Bound State in a Scalar Model

We use the worldline representation of field theory together with a variational approximation to determine the lowest bound state in the scalar Wick-Cutkosky model where two equal-mass constituents interact via the exchange of mesons. Self-energy and vertex corrections are included approximately in a consistent way as well as crossed diagrams. Only vacuum-polarization effects of the heavy particles are neglected. In a path integral description of an appropriate current-current correlator an effective, retarded action is obtained by integrating out the meson field. As in the polaron problem we employ a quadratic trial action with variational functions to describe retardation and binding effects through multiple meson exchange.The variational equations for these functions are derived, discussed qualitatively and solved numerically. We compare our results with the ones from traditional approaches based on the Bethe-Salpeter equation and find an enhanced binding contrary to some claims in the literature. For weak coupling this is worked out analytically and compared with results from effective field theories. However, the well-known instability of the model, which usually is ignored, now appears at smaller coupling constants than in the one-body case and even when self-energy and vertex corrections are turned off. This induced instability is investigated analytically and the width of the bound state above the critical coupling is estimated.Comment: 62 pages, 7 figures, FBS style, published versio

Solution of coupled vertex and propagator Dyson-Schwinger equations in the scalar Munczek-Nemirovsky model

In a scalar $\phi^2\chi$ model, we exactly solve the vertex and $\phi$ propagator Dyson-Schwinger equations under the assumption of a spatially constant (Munczek-Nemirovsky) propagator for the $\chi$ field. Various truncation schemes are also considered.Comment: 7 pages,4 figures, minor changes, reference added for published versio

The chicken or the egg; or Who ordered the chiral phase transition?

We draw an analogy between the deconfining transition in the 2+1 dimensional Georgi-Glashow model and the chiral phase transition in 3+1 dimensional QCD. Based on the detailed analysis of the former (hep-th/0010201) we suggest that the chiral symmetry restoration in QCD at high temperature is driven by the thermal ensemble of baryons and anti-baryons. The chiral symmetry is restored when roughly half of the volume is occupied by the baryons. Surprisingly enough, even though baryons are rather heavy, a crude estimate for the critical temperature gives $T_c=180$ Mev. In this scenario the binding of the instantons is not the cause but rather a consequence of the chiral symmetry restoration.Comment: 22 pages, 7 figures, comments about chiral symmetry at finite nuclear density are adde

Intrinsic quadrupole moment of the nucleon

We address the question of the intrinsic quadrupole moment Q_0 of the nucleon in various models. All models give a positive intrinsic quadrupole moment for the proton. This corresponds to a prolate deformation. We also calculate the intrinsic quadrupole moment of the Delta(1232). All our models lead to a negative intrinsic quadrupole moment of the Delta corresponding to an oblate deformation.Comment: 17 pages, 5 figure

Baryon Charge Radii and Quadrupole Moments in the 1/N_c Expansion: The 3-Flavor Case

We develop a straightforward method to compute charge radii and quadrupole moments for baryons both with and without strangeness, when the number of QCD color charges is N_c. The minimal assumption of the single-photon exchange ansatz implies that only two operators are required to describe these baryon observables. Our results are presented so that SU(3) flavor and isospin symmetry breaking can be introduced according to any desired specification, although we also present results obtained from two patterns suggested by the quark model with gluon exchange interactions. The method also permits to extract a number of model-independent relations; a sample is r^2_Lambda / r_n^2 = 3/(N_c+3), independent of SU(3) symmetry breaking.Comment: 30 pages, no figures, REVTeX