19 research outputs found
Study of relativistic bound states for scalar theories in Bethe-Salpeter and Dyson-Schwinger formalism
The Bethe-Salpeter equation for Wick-Cutkosky like models is solved in
dressed ladder approximation. The bare vertex truncation of the Dyson-Schwinger
equations for propagators is combined with the dressed ladder Bethe-Salpeter
equation for the scalar S-wave bound state amplitudes. With the help of
spectral representation the results are obtained directly in Minkowski space.
We give a new analytic formula for the resulting equation simplifying the
numerical treatment. The bare ladder approximation of Bethe-Salpeter equation
is compared with the one with dressed ladder. The elastic electromagnetic form
factors is calculated within the relativistic impulse approximation.Comment: 30 pages, 10 figures, accepted for publication in Phys. Rev.
Solving the Bethe-Salpeter equation for a pseudoscalar meson in Minkowski space
A new method of solution of the Bethe-Salpeter equation for a pseudoscalar
quark-antiquark bound state is proposed. With the help of an integral
representation, the results are directly obtained in Minkowski space. Dressing
of Green's functions is naturally taken into account, thus providing the
possible inclusion of a running coupling constant as well as quark propagators.
First numerical results are presented for a simplified ladder approximation
Schwinger functions and light-quark bound states
We examine the applicability and viability of methods to obtain knowledge
about bound-states from information provided solely in Euclidean space.
Rudimentary methods can be adequate if one only requires information about the
ground and first excited state and assumptions made about analytic properties
are valid. However, to obtain information from Schwinger functions about higher
mass states, something more sophisticated is necessary. A method based on the
correlator matrix can be dependable when operators are carefully tuned and
errors are small. This method is nevertheless not competitive when an
unambiguous analytic continuation of even a single Schwinger function to
complex momenta is available.Comment: 27 pages, 14 figure
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
Implications of analyticity to solution of Schwinger-Dyson equations in Minkowski space
We review some recent developments in nonperturbative studies of quantum
field theory (QFT) using the Schwinger-Dyson equations formulated directly in
Minkowski space. We begin with the introduction of essential ideas of the
integral representation in QFT and a discussion of renormalization in this
approach. The technique based on the integral representation of Green's
functions is exploited to solve Schwinger-Dyson equations in several quantum
field models, eg. in scalar models and in strong coupling in the
quenched and in the unquenched approximation. The phenomenon of dynamical
chiral symmetry breaking in regularized theory is touched. In QCD, the
analyticity of gluon propagator on the complex momentum square plane is
exploited to continue some recent lattice data to timelike momentum axis. We
find non-positive absorptive part contribution in the Landau gauge gluon
propagator which is in agreement with some other new recent analyzes.Comment: 57 pages, Sections slightly reorganized, one section devoted to CHSB
added, references changed, accepted in Few-body System
Quark Schwinger-Dyson equation in temporal Euclidean space
We present an elementary nonperturbative method to obtain Green's functions
(GFs) for timelike momenta. We assume there are no singularities in the first
and third quadrants of the complex plane of space momentum components and
perform a 3d analogue of Wick rotation. This procedure defines Greens functions
in a timelike Euclidean space. As an example we consider the quark propagator
in QCD. While for weak coupling, this method is obviously equivalent to
perturbation theory, for a realistic QCD coupling a complex part of the quark
mass and renormalization wave function has been spontaneously generated even
below the standard perturbative threshold. Therefore, our method favors a
confinement mechanism based on the lack of real poles.Comment: 11 pages, grammar and typos correcte
The MHD nature of ionospheric wave packets excited by the solar terminator
We obtained the first experimental evidence for the magnetohydrodynamic (MHD)
nature of ionospheric medium-scale travelling wave packets (MSTWP). We used
data on total electron content (TEC) measurements obtained at the dense
Japanese network GPS/GEONET (1220 stations) in 2008-2009. We found that the
diurnal, seasonal and spectral MSTWP characteristics are specified by the solar
terminator (ST) dynamics. MSTWPs are the chains of narrow-band TEC oscillations
with single packet's duration of about 1-2 hours and oscillation periods of
10-20 minutes. Their total duration is about 4--6 hours. The MSTWP spatial
structure is characterized by a high degree of anisotropy and coherence at the
distance of more than 10 wavelengths. The MSTWP direction of travelling is
characterized by a high directivity regardless of seasons. Occurrence rate of
daytime MSTWPs is high in winter and during equinoxes. Occurrence rate of
nighttime MSTIDs has its peak in summer. These features are consistent with
previous MS travelling ionosphere disturbance (TID) statistics obtained from
630-nm airglow imaging observations in Japan. In winter, MSTWPs in the northern
hemisphere are observed 3-4 hours after the morning ST passage. In summer,
MSTWPs are detected 1.5-2 hours before the evening ST occurrence at the point
of observations, at the moment of the evening ST passage in the
magneto-conjugate point. Both the high Q-factor of oscillatory system and
synchronization of MSTWP occurrence with the solar terminator passage at the
point of observations and in the magneto-conjugate area testify the MHD nature
of ST-excited MSTWP generation. The obtained results are the first experimental
evidence for the hypothesis of the ST-generated ion sound waves.Comment: 12 pages, 3 figure
Persistence of the planetary wave type oscillations in <i>fo</i>F2 over Europe
Planetary waves are
oscillations of very predominantly tropospheric origin with typical periods of
about 2–30 days. Their dominant zonal wave numbers are 1, 2 and 3, i.e. the
waves are of large-scale (global) character. The planetary wave type
oscillations have been observed in the lower and middle atmosphere but also in
the ionosphere, including the ionospheric F2-layer. Here, we deal only with the
oscillations analyzed for four European stations over a solar cycle with the
use of the Meyer and Morlet wavelet transforms. Waves with periods near 5, 10
and 16 days are studied. Only events with a duration of three wave-cycles and
more are considered. The 5-day period wave events display a typical duration of
4 cycles, while 10- and 16-day wave events are less persistent, with a typical
duration of about 3.5 cycles and 3 cycles, respectively. The persistence
pattern in terms of number of cycles and in terms of number of days is
different. In terms of number of cycles, the typical persistence of
oscillations decreases with increasing period. On the other hand, in terms of
number of days the typical persistence evidently increases with increasing
period. The spectral distribution of event duration is too broad to allow for a
reasonable prediction of event duration. Thus, the predictability of the
planetary wave type oscillations in foF2 seems to be very questionable.Key words. Ionosphere
(ionosphere-atmosphere interaction, mid-latitude ionosphere, ionospheric
disturbances) – Meteorology and atmospheric dynamics (waves and tides