David Wallace

Brian Pitts has recently claimed to show via straightforward calculation that, at least in the case of Hamiltonian electromagnetism, an arbitrary first-class constraint ``generates not a gauge transformation, but a bad physical change'' (Annals of Physics 351 (2014) pp.382-406; arXiv:1310.2756). We show, via a straightforward calculation, that a transformation generated by an arbitrary first-class constraint relates gauge-equivalent phase space points, vindicating orthodoxy. Pitts, however, is primarily concerned with transformations of entire histories, rather than of instantaneous states. We show that, even in this context, a transformation generated by an arbitrary first-class constraint is also a gauge transformation, once the empirically observed electric field is correctly identified via its dynamical interactions with charge, and not simply given stipulatively as a certain combination of the potential and its derivatives.

The working assumption amongst most philosophers of QFT appears to be that algebraic QFT, and not the "Lagrangian" QFT of the working physicist, is the proper object of philosophical and foundational study. I argue that this assumption is unmotivated, and fails to take into account important features of the post-1960s development of Lagrangian QFT. From a modern perspective the two forms of QFT are better seen as rival research programs than as variant formulations of one theory; furthermore, the Lagrangian research program is overwhelmingly supported by experiment.