Letters in Mathematical Physics

, Volume 109, Issue 12, pp 2601–2610 | Cite as

On string-localized potentials and gauge fields

  • Detlev BuchholzEmail author
  • Fabio Ciolli
  • Giuseppe Ruzzi
  • Ezio Vasselli


A recent idea, put forward by Mund, Rehren and Schroer, is discussed; it suggests that in gauge quantum field theory, one can replace the point-localized gauge fields by string-localized vector potentials built from gauge-invariant observables and a principle of string independence. Based on a kinematical model, describing unmovable (static) fields carrying opposite charges, it is shown that these string-localized potentials cannot be used for the description of the gauge bridges between electrically charged fields. These bridges are needed in order to ensure the validity of Gauss’s law. This observation does not preclude the existence of Poincaré invariant theories, describing the coupling of string-localized gauge-invariant potentials to matter fields. But these potentials are not a full-fledged substitute for the gauge fields in “usual” quantum electrodynamics.


Gauge bridges String-localized observable potentials Gauss’s law 

Mathematics Subject Classification

81T05 83C47 57T15 



DB gratefully acknowledges the hospitality and support extended to him by Roberto Longo and the University of Rome “Tor Vergata,” which made this collaboration possible. FC and GR are supported by the ERC Advanced Grant 669240 QUEST “Quantum Algebraic Structures and Models.” EV is supported in part by OPAL “Consolidate the Foundations.” All authors acknowledge support by the MIUR Excellence Department Project, awarded to the Department of Mathematics, University of Rome Tor Vergata, CUP E83C18000100006.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität GöttingenGöttingenGermany
  2. 2.Dipartimento di MatematicaUniversitá di Roma “Tor Vergata”RomeItaly

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