I hope this
presentation has demonstrated that
realistic potentials ( with a minimum number of parameters —three or less) can be derived using nonlinear pion meson
fields. The SG SWEP was used as an example. However, most people prefer
the lF4 SWEP. It
yields almost identical results as the SG SWEP.
More general nonlinear extensions
to the Klein Gordon equation of the form l1F2p+1+l2F4p+1 exist. (See Burt’s webpage and references there in) .
Burt has found a simple mass formula for pseudoscalar mesons :
Mn = (3n+1)mp n= 0, 1,2, 3… , mp is the pion mass. This formula is obtained from the poles of the propagator based on the equation
¶m¶mF+m2F+l1F5+l2 F7=0.
It will be
interesting to derive and test a corresponding SWEP It may also be necessary to
incorporate r and
w mesons.
Vector meson can contribute thge missing VLS term. The r meson can also weaken the strong pion tensor contribution. The Hamburg nuclear theory group has done all these and more. However, they also include two fictitious s mesons. This may not be necessary. With an
appropriate choice of the self interaction coupling constants, SWEPs can provide sufficient intermediate
attraction. Fictitious one or more s mesons are used to simulate multi-meson exchanges in OBEPs.
Once
expressions for SWEPs are derived, it is possible to involve undergraduate students in the
physical science to do most of the work.