In this paper we study non-standard neutrino interactions as an example of
physics beyond the standard model using atmospheric neutrino data collected
during the Super-Kamiokande I(1996-2001) and II(2003-2005) periods. We focus on
flavor-changing-neutral-currents (FCNC), which allow neutrino flavor
transitions via neutral current interactions, and effects which violate lepton
non-universality (NU) and give rise to different neutral-current
interaction-amplitudes for different neutrino flavors. We obtain a limit on the
FCNC coupling parameter, varepsilon_{mu tau}, |varepsilon_{mu tau}|<1.1 x
10^{-2} at 90%C.L. and various constraints on other FCNC parameters as a
function of the NU coupling, varepsilon_{e e}. We find no evidence of
non-standard neutrino interactions in the Super-Kamiokande atmospheric data.Comment: 12 Pages, 14 figures. To be submitted to Phys. Rev.