84 research outputs found
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
A new Fermi smearing approach for scattering of multi-GeV electrons by nuclei
The cross section for electron scattering by nuclei at high momentum
transfers is calculated within the Fermi smearing approximation (FSA), where
binding effects on the struck nucleon are introduced via the relativistic
Hartree approximation (RHA). The model naturally preserves current
conservation, since the response tensor for an off-shell nucleon conserves the
same form that for a free one but with an effective mass. Different
parameterizations for the inelastic nucleon structure function, are analyzed.
The smearing at the Fermi surface is introduced through a momentum distribution
obtained from a perturbative nuclear matter calculation. Recent CEBAF data on
inclusive scattering of 4.05 GeV electrons on Fe are well reproduced for
all measured geometries for the first time, as is evident from the comparison
with previous calculations.Comment: 8 pages in Revtex4 style, 6 eps figures, to appear in Physical Review
Variational Approximations in a Path-Integral Description of Potential Scattering
Using a recent path integral representation for the T-matrix in
nonrelativistic potential scattering we investigate new variational
approximations in this framework. By means of the Feynman-Jensen variational
principle and the most general ansatz quadratic in the velocity variables --
over which one has to integrate functionally -- we obtain variational equations
which contain classical elements (trajectories) as well as quantum-mechanical
ones (wave spreading).We analyse these equations and solve them numerically by
iteration, a procedure best suited at high energy. The first correction to the
variational result arising from a cumulant expansion is also evaluated.
Comparison is made with exact partial-wave results for scattering from a
Gaussian potential and better agreement is found at large scattering angles
where the standard eikonal-type approximations fail.Comment: 35 pages, 3 figures, 6 tables, Latex with amsmath, amssymb; v2: 28
pages, EPJ style, misprints corrected, note added about correct treatment of
complex Gaussian integrals with the theory of "pencils", matches published
versio
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.
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
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
Worldline path integral for the massive Dirac propagator : A four-dimensional approach
We simplify and generalize an approach proposed by Di Vecchia and Ravndal to
describe a massive Dirac particle in external vector and scalar fields. Two
different path integral representations for the propagator are derived
systematically without the usual five-dimensional extension and shown to be
equivalent due to the supersymmetry of the action. They correspond to a
projection on the mass of the particle either continuously or at the end of the
time evolution. It is shown that the supersymmetry transformations are
generated by shifting and scaling the supertimes and the invariant difference
of two supertimes is given for the general case. A nonrelativistic reduction of
the relativistic propagator leads to a three-dimensional path integral with the
usual Pauli Hamiltonian. By integrating out the photons we obtain the effective
action for quenched QED and use it to derive the gauge-transformation
properties of the general Green function of the theory.Comment: 27 pages, LaTeX, no figures, uses revtex.sty; note with omitted
references added in proo
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
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
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