PCT, Spin, Lagrangians, Part II

I promised a second part. Here it is. I hesitated, because I don’t like being destructive, and unfortunately, to deal with the current state of affairs in quantum theory means just doing this: I show you that the current gauge theory is fundamentally ill-designed, along with it fall Weinberg model and Wightman theory. 1. Continuing with the Lagrangian Formalism Let me continue from where I left off in the former part: As we saw, the Lagrangian formalism for what is conceived to be the free quantum field amounts to evaluate the extremal for δ < φ,Aφ > with A := (1/2)( φ−m2). Now, A is a self-adjoint operator, and for that operator it is plain vanilla that the kernel of A is the space of the extremals of < φ,Aφ >, and in this case happens to be the space of solutions of the Klein-Gordon equation φ−m2φ = 0. The problem in here is that from φ−m2φ = 0 it cannot be concluded that L := (−1/2) ( < ∂μφ, ∂ φ > − < φ,m2φ > ) or any of its equivalent reformulations is the correct Lagrangian: A can be anything, for example the square or n-th power of A have the same kernel, but they would define different Lagrangians. (In [6] I showed that there are two distinct Lagrangians solving the very same equation of motion. Now we see that there are arbitarily many. Besides this: Does mxμ for 0 ≤ μ ≤ 3 possess the dimension of an action? No! But mxμ does! The Lagrangian Formalism is simply meaningless!