Construction and applications of Lorentz-violating nonabelian gauge field theories

Lorentz violation can emerge in certain theoretical schemes unifying General Relativity and the Standard Model, and it is a popular candidate for modifications to low-energy physics. The Standard-Model Extension (SME) is a comprehensive framework for describing Lorentz violation in the context of realistic effective field theory. All minimal SME operators are known, but the explicit construction of possible nonminimal operators of arbitrary mass dimension has been an open issue. In this talk, we present a method to construct arbitrary gauge-invariant Lorentz-violating operators in nonabelian field theories. Applied to quantum electrodynamics and quantum chromodynamics, the method establishes the Lagrange densities for Lorentz-violating QED and QCD. We study implications of these theories for experiments involving light-by-light scattering and deep inelastic scattering, and we use existing data to obtain first bounds on certain nonminimal SME coefficients.