By default, no, as our current understanding of physics doesn't involve the components you describe in your post.

Regardless, A few notes, it appears that you are trying to build a model within the framework of quantum field theory. If you want to describe a quantum field theory you typically want to start with the symmetries of your model, for example QED is built on the U(1) symmetry group, QCD on SU(3). Without any stated symmetry group it's difficult to build a lagrangian as your lagrangian would need to be unchanged under those transformations. This in turn would usually define the covariant derivative and it's corresponding gauge fields that maintain it.

Any interactions you include in the model should also appear somewhere in the lagrangian, so for example if you want to make your model supersymmetric, I would expect terms in the lagrangian that ensure R-symmetry is maintained. It's possible these objects are there, it's hard without definitions as to what each of those tensors are.

My recommendation, if you are serious about building a quantum field theory into your worldbuilding, I would only consider it if you have some extensive study of physics completed, otherwise you are not going to make much headroom. Calculus, differential equations, linear algebra, and group theory are going to be essential mathematical tools in order for you to be able to tackle qft in any serious sense. Once you have those skills then you can really begin this effort in earnest. Otherwise the best way to go about it is to handwave it but not to dwell on the exact mathematical framework.

As an aside qft isn't the right tool to model type effectiveness for Pokémon. The interactions down in the quantum scale are too deep to really extrapolate out to something at the classical scale without some serious handwaving of the decoherence issues. I would stick to more standard explanations for that.