  We use the Chern-Simons quantum field theory in order to prove a recently
conjectured limitation on the 1/K expansion of the Jones polynomial of a knot
and its relation to the Alexander polynomial. This limitation allows us to
derive a surgery formula for the loop corrections to the contribution of the
trivial connection to Witten's invariant. The 2-loop part of this formula
coincides with Walker's surgery formula for Casson-Walker invariant. This
proves a conjecture that Casson-Walker invariant is a 2-loop correction to the
trivial connection contribution to Witten's invariant of a rational homology
sphere. A contribution of the trivial connection to Witten's invariant of a
manifold with nontrivial rational homology is calculated for the case of
Seifert manifolds.
