71 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
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.
Color transparency in deeply inelastic diffraction
We suggest a simple physical picture for the diffractive parton distributions
that appear in diffractive deeply inelastic scattering. In this picture,
partons impinging on the proton can have any transverse separation, but only
when the separation is small can they penetrate the proton without breaking it
up. By comparing the predictions from this picture with the diffractive data
from HERA, we determine rough values for the small separations that dominate
the diffraction process.Comment: 10 pages, 2 figures; v2: citations added, two comments revised and
expanded, results unchange
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
Nonperturbative dynamics of scalar field theories through the Feynman-Schwinger representation
In this paper we present a summary of results obtained for scalar field
theories using the Feynman-Schwinger (FSR) approach. Specifically, scalar QED
and chi^2phi theories are considered. The motivation behind the applications
discussed in this paper is to use the FSR method as a rigorous tool for testing
the quality of commonly used approximations in field theory. Exact calculations
in a quenched theory are presented for one-, two-, and three-body bound states.
Results obtained indicate that some of the commonly used approximations, such
as Bethe-Salpeter ladder summation for bound states and the rainbow summation
for one body problems, produce significantly different results from those
obtained from the FSR approach. We find that more accurate results can be
obtained using other, simpler, approximation schemes.Comment: 25 pags, 19 figures, prepared for the volume celebrating the 70th
birthday of Yuri Simono
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
Proton Zemach radius from measurements of the hyperfine splitting of hydrogen and muonic hydrogen
While measurements of the hyperfine structure of hydrogen-like atoms are
traditionally regarded as test of bound-state QED, we assume that theoretical
QED predictions are accurate and discuss the information about the
electromagnetic structure of protons that could be extracted from the
experimental values of the ground state hyperfine splitting in hydrogen and
muonic hydrogen. Using recent theoretical results on the proton polarizability
effects and the experimental hydrogen hyperfine splitting we obtain for the
Zemach radius of the proton the value 1.040(16) fm. We compare it to the
various theoretical estimates the uncertainty of which is shown to be larger
that 0.016 fm. This point of view gives quite convincing arguments in support
of projects to measure the hyperfine splitting of muonic hydrogen.Comment: Submitted to Phys. Rev.
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
The Generalized Gell-Mann--Low Theorem for Relativistic Bound States
The recently established generalized Gell-Mann--Low theorem is applied in
lowest perturbative order to bound-state calculations in a simple scalar field
theory with cubic couplings. The approach via the generalized Gell-Mann--Low
Theorem retains, while being fully relativistic, many of the desirable features
of the quantum mechanical approaches to bound states. In particular, no
abnormal or unphysical solutions are found in the model under consideration.
Both the non-relativistic and one-body limits are straightforward and
consistent. The results for the spectrum are compared to those of the
Bethe-Salpeter equation (in the ladder approximation) and related equations.Comment: 24 pages, 6 pspicture diagrams, 4 postscript figure
Proton polarizability effect in the Lamb shift of the hydrogen atom
The proton polarizability correction to the Lamb shift of electronic and
muonic hydrogen is calculated on the basis of isobar model and experimental
data on the structure functions of deep inelastic lepton-nucleon scattering.
The contributions of the Born terms, vector-meson exchanges and nucleon
resonances are taken into account in the construction of the photoabsorption
cross sections for transversely and longitudinally polarized virtual photons
sigma_{T,L}.Comment: 11 pages, 3 figure
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