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On The Ladder Bethe-Salpeter Equation
The Bethe-Salpeter (BS) equation in the ladder approximation is studied
within a scalar theory: two scalar fields (constituents) with mass
interacting via an exchange of a scalar field (tieon) with mass . The BS
equation is written in the form of an integral equation in the configuration
Euclidean -space with the kernel which for stable bound states is a
self-adjoint positive operator. The solution of the BS equation is formulated
as a variational problem. The nonrelativistic limit of the BS equation is
considered. The role of so-called abnormal states is discussed. The analytical
form of test functions for which the accuracy of calculations of bound state
masses is better than 1% (the comparison with available numerical calculations
is done) is determined. These test functions make it possible to calculate
analytically vertex functions describing the interaction of bound states with
constituents. As a by-product a simple solution of the Wick-Cutkosky model for
the case of massless bound states is demonstrated
Glueball as a bound state in the self-dual homogeneous gluon field
Using a simple relativistic QFT model of scalar fields we demonstrate that
the analytic confinement (propagator is an entire function in the complex
--plane) and the weak coupling constant lead to the Regge behaviour of the
two-particle bound states. In QCD we assume that the gluon vacuum is realized
by the self-dual homogeneous classical field which is the solution of the
Yang-Mills equations. This assumption leads to analytical confinement of quarks
and gluons. We extract the colorless two-gluon state from the QCD
generating functional in the one-gluon exchange approximation. The mass of this
bound state is defined by the Bethe-Salpeter equation. The glueball mass is
for if the gluon condensate is
.Comment: 3 pages. Parallel talk given at the 5rd International Conference on
Quark Confinement and the Hadron Spectrum (Confinement V), Gargnano, Italy,
September 10-14, 2002. To appear in the proceeding
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