In searching for indications of new physics scalar particle and unparticle
couplings in e^+ e^- \to t\bar t, we consider the role of transversely
polarized initial beams at e^+ e^- colliders. By using a general relativistic
spin density matrix formalism for describing the particles spin states, we find
analytical expressions for the squared amplitude of the process with t or \bar
t polarization measured, including the anomalous coupling contributions. Thanks
to the transversely polarized initial beams these contributions are first order
anomalous coupling corrections to the Standard Model (SM) contributions. We
present and analyse the main features of the SM and anomalous coupling
contributions. We show how differences between SM and anomalous coupling
contributions provide means to search for anomalous coupling manifestations at
future e^+ e^- linear colliders.Comment: 28 pages in LaTeX, including 7 encapsulated PostScript figures,
published versio