Hidden gauge invariance

Abstract: The role of gauge invariance is reconsidered by "deriving it without assuming it" within an autonomous approach to interactions of Standard Model particles. In this approach, the renormalizable interactions are purely constrained by quantum principles, notably the representation on a Hilbert space. It is shown that - surprisingly - most interactions fulfilling the constraints enjoy a "hidden" gauge invariance (uncovered via redefinitions of quantum fields). The hidden gauge invariance is exact and unbroken even in the presence of massive vector bosons. While the Hilbert space formulation requires the use of "string-localized interactions", its role is to secure that S-matrices are string-independent, and in fact coincide with S-matrices with local interactions from the gauge theory approach on indefinite state spaces. Thus, particle physics with massless and massive vector bosons can be understood without neither indefinite state spaces nor ghosts.