I am going to talk about my recent works on the topic of operator j-basis, which is an independent basis of effective operators that are related to partial wave amplitudes. The project is embedded in the Amplitude Basis program that studies different operator bases of the effective field theories (EFT) and their applications. The j-basis operator features definite quantum numbers, including the angular momentum, for particular partitions of the constituting fields. An important prerequisite technique is to generalize the definition of partial waves for scattering amplitude among arbitrary number of particles. The symmetries of the EFT impose non-inteference between the operators with different quantum numbers. I will show the important role of the j-basis in the loop amplitudes, renormalization and the tree-level UV origin of the effective operators.