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Shock-free wave propagation in gauge theories

We present the shock-free wave propagation requirements for massless fields. First, we briefly argue how the "completely exceptional" approach, originally developed to study the characteristics of hyperbolic systems in 1 + 1 dimensions, can be generalized to higher dimensions and used to describe propagation without emerging shocks, with characteristic flow remaining parallel along the waves. We then study the resulting requirements for scalar, vector, vector-scalar, and gravity models and characterize physically acceptable actions in each case.