I analyse the conceptual and mathematical foundations of Lagrangian quantum field theory (that is, the ‘naive’ quantum field theory used in mainstream physics, as opposed to algebraic quantum field theory). The objective is to see whether Lagrangian quantum field theory has a sufficiently firm conceptual and mathematical basis to be a legitimate object of foundational study, or whether it is to...

These notes were prepared as a support for a talk at the graduate workshop ”Supersymmetric Field Theories and Their Mathematical Implications” held in March 2012 at the Simons Center in Stony Brook. They are essentially cut out of [1], from which nearly all the material is taken, with a little rearrangement. To the reader looking for a richer exposition we definitely suggest the excellent sourc...

τ decays into hadrons have a twofold interest: On the one hand, they are a clean environment for studying the hadronization of the left-handed current of QCD, while, on the other side, provide relevant dynamical information of the resonances that mediate these processes. Within an effective field theory-like framework, namely Resonance Chiral Theory, we analyse the decays ot the τ into KKπ mode...