Gauge invariant propagators and states in quantum electrodynamics

We study combined matter/gauge field gauge invariant states in terms of data living on the boundary of gauge invariant path-integrals. To get concrete results, this is done for scalar and spinor QED, for both 'time-slice', and 'causal diamond' boundaries. We discuss both the standard case where the gauge field falls off to zero at the spatial boundaries, and the case of 'large gauge transformations', where it remains finite at these boundaries. The path-integral naturally generates a specific dressing factor for states living on time-slices, without fixing any gauge, and we identify a universal contribution which depends only on the nature of the boundaries. We also derive the analogous dressing for states defined on null infinity, showing both its Coulombic parts as well as soft-photon parts. ; © 2022 Elsevier. Received 19 January 2022, Accepted 1 May 2022, Available online 9 May 2022. This work was funded in Canada by the National Science and Engineering Research Council of Canada (NSERC). In the USA, PCES received support at Caltech from the Simons Foundation, USA (Award 568762) and the National Science Foundation, USA (Award PHY-1733907). JWG was additionally supported by a NSERC PGS-D award in Canada, and a Burke Fellowship at Caltech. We have benefited particularly from extended discussions with C Delisle at UBC. We also thank W.G. Unruh at UBC and Y. Chen at Caltech for illuminating remarks. We would also like to acknowledge the support and hospitality of Y. Chen, T.F. Rosenbaum, and K.S. Thorne at Caltech. CRediT authorship contribution statement: Jordan Wilson-Gerow: Conceptualization, Methodology, Validation, Writing – original draft, Writing – review & editing, Visualization, Supervision, Project administration, Funding acquisition. P.C.E. Stamp: Conceptualization, Methodology, Validation, Writing – original draft, Writing – review & editing, Visualization, Supervision, Project administration, Funding acquisition. The authors declare that they have no known competing financial interests or ...