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We consider a theory of scalar and spinor fields, interacting through Yukawa and ϕ4 interactions, with Lorentz-violating operators included in the Lagrangian. We compute the leading quantum corrections in this theory. The renormalizability of the theory is explicitly shown up to one-loop order. In the pure scalar sector, the calculations can be generalized to higher orders and to include finite terms, because the theory can be solved in terms of its Lorentz-invariant version.

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Ferrero, A., & Altschul, B. (2011). Renormalization of scalar and Yukawa field theories with Lorentz violation. Physical Review D, 84(6).

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