  Neutrino oscillations are precision probes of new physics beyond the Standard
Model. Apart from neutrino masses and mixings, they are also sensitive to
possible deviations of low-energy interactions between quarks and leptons from
the Standard Model predictions. In this paper we develop a systematic
description of such non-standard interactions (NSI) in oscillation experiments
within the quantum field theory framework. We calculate the event rate and
oscillation probability in the presence of general NSI, starting from the
effective field theory (EFT) in which new physics modifies the flavor or
Lorentz structure of charged-current interactions between leptons and quarks.
We also provide the matching between the EFT Wilson coefficients and the widely
used simplified quantum-mechanical approach, where new physics is encoded in a
set of production and detection NSI parameters. Finally, we discuss the
consistency conditions for the standard NSI approach to correctly reproduce the
quantum field theory result.
