Properties of the linearized functional renormalization group

Interactions growing slower than a certain exponential of the square scalar field are well behaved when evolved under functional renormalization group linearized around Gaussian fixed point. They satisfy properties usually taken for granted, and reproduce standard perturbative quantization. However, more challenging effects appear, interactions grow faster this. We show explicitly that firstly, flow no longer splits uniquely into operators definite scaling dimension; secondly, (linearized) flows to infrared can end prematurely in singularity; finally, new spontaneously appear at any scale.