Beware that besides the Lorentz group, a field can transform under the action of a gauge group. For example, a scalar field ϕ ϕ ( x ) , where x is a spacetime point, might have an isospin state taking values in the fundamental representation C 2 of SU ( 2 ) . Then ϕ ϕ ( x ) is a vector valued function of spacetime, but is still referred to as a scalar field, as it transforms trivially under Lorentz transformations.