Transverse muon polarization in K+ -> mu+ nu_mu gamma: scanning over the Dalitz plot

We study the potential of the measurement of the transverse muon polarization P_T in the K->mu nu gamma decay with the sensitivity of \delta P_T ~ 10^{-4}. It is shown that the forthcoming experiment can measure the contribution of the electromagnetic final state interactions to P_T that gives a possibility to unambiguously determine the signs of the sum of the kaon form factors F_V and F_A even without fixing their difference. We also estimate the sensitivity of this experiment to the new physics, which could give rise to T-violation: multi-Higgs doublet models, supersymmetric extensions of the Standard Model, left-right symmetric model and leptoquark models.