  A generalized top-spin analysis proposed some time ago in the context of
Standard Model and subsequently studied in varying contexts is now applied
primarily to the case of $e^+e^-\rightarrow t\bar{t}$ with transversely
polarized beams. This extends our recent work with new physics couplings of
scalar ($S$) and tensor ($T$) types. We carry out a comprehensive analysis
assuming only the electron beam to be transversely polarized, which is
sufficient to probe these interactions, and also eliminates any azimuthal
angular dependence due to standard model or new physics of vector ($V$) and
axial-vector ($A$) type interactions. We then consider new physics of general
four-Fermi type of $V$ and $A$ type with both beams transversely polarized and
discuss implications with longitudinal polarization as well. The generalized
spin bases are all investigated in the presence of either longitudinal or
transverse beam polarization to look for appreciable deviation from the SM
prediction in case of the new physics. 90% confidence level limits are obtained
on the interactions for the generalized spin bases with realistic integrated
luminosity. In order to achieve this we present a general discussion based on
helicity amplitudes and derive a general transformation matrix that enables us
to treat the spin basis. We find that beamline basis combined with transverse
polarization provides an excellent window of opportunity both for $S$, $T$ and
$V$, $A$ new physics, followed by the off diagonal basis. The helicity basis is
shown to be the best in case of longitudinal polarization to look for new
physics effectsdue to $V$ and $A$.
