111 research outputs found
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 -Matrix in Nonrelativistic Potential Scattering
Several path integral representations for the -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 model, we exactly solve the vertex and
propagator Dyson-Schwinger equations under the assumption of a spatially
constant (Munczek-Nemirovsky) propagator for the 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 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
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