4 research outputs found
Study of Quark Propagator Solutions to the Dyson--Schwinger Equation in a Confining Model
We solve the Dyson--Schwinger equation for the quark propagator in a model
with singular infrared behavior for the gluon propagator. We require that the
solutions, easily found in configuration space, be tempered distributions and
thus have Fourier transforms. This severely limits the boundary conditions that
the solutions may satisify. The sign of the dimensionful parameter that
characterizes the model gluon propagator can be either positive or negative. If
the sign is negative, we find a unique solution. It is singular at the origin
in momentum space, falls off like as , and it
is truly nonperturbative in that it is singular in the limit that the
gluon--quark interaction approaches zero. If the sign of the gluon propagator
coefficient is positive, we find solutions that are, in a sense that we
exhibit, unconstrained linear combinations of advanced and retarded
propagators. These solutions are singular at the origin in momentum space, fall
off like asympotically, exhibit ``resonant--like" behavior at the
position of the bare mass of the quark when the mass is large compared to the
dimensionful interaction parameter in the gluon propagator model, and smoothly
approach a linear combination of free--quark, advanced and retarded two--point
functions in the limit that the interaction approaches zero. In this sense,
these solutions behave in an increasingly ``particle--like" manner as the quark
becomes heavy. The Feynman propagator and the Wightman function are not
tempered distributions and therefore are not acceptable solutions to the
Schwinger--Dyson equation in our model. On this basis we advance several
arguments to show that the Fourier--transformable solutions we find are
consistent with quark confinement, even though they have singularities on th
Gauge covariant fermion propagator in quenched, chirally-symmetric quantum electrodynamics
We discuss the chirally symmetric solution of the massless, quenched,
Dyson-Schwinger equation for the fermion propagator in three and four
dimensions. The solutions are manifestly gauge covariant. We consider a gauge
covariance constraint on the fermion--gauge-boson vertex, which motivates a
vertex Ansatz that both satisfies the Ward identity when the fermion self-mass
is zero and ensures gauge covariance of the fermion propagator.Comment: 11 pages. REVTEX 3.0. ANL-PHY-7711-TH-9