Symmetry groups of scalar relativistic fields with self-interaction

The symmetry groups of a relativistically invariant quasilinear second-order equation of the most general form are investigated. The problem of group classification is solved: all the additional Lie symmetry groups of transformations of the dependent variable and the independent variables admitted by each of all possible types of equation are found. In particular, the following are found: two types of new conformally invariant equations, equations that are invariant under an inhomogeneous group of motions in a space with one dimension more than the original space, and equations that admit infinite groups. They all describe fields with anomalous scale dimension. The conserved currents are constructed for Lagrangian equations.