Gauss’ Law and string-localized quantum field theory

@article{Mund2020GaussLA,
  title={Gauss’ Law and string-localized quantum field theory},
  author={Jens Mund and Karl-Henning Rehren and Bert Schroer},
  journal={Journal of High Energy Physics},
  year={2020},
  volume={2020},
  pages={1-27}
}
A bstractThe quantum Gauss Law as an interacting field equation is a prominent feature of QED with eminent impact on its algebraic and superselection structure. It forces charged particles to be accompanied by “photon clouds” that cannot be realized in the Fock space, and prevents them from having a sharp mass [7, 19]. Because it entails the possibility of “measurement of charges at a distance”, it is well-known to be in conflict with locality of charged fields in a Hilbert space [3, 17]. We… 
Quantum Electrostatics, Gauss’s Law, and a Product Picture for Quantum Electrodynamics; or, the Temporal Gauge Revised
We provide a theoretical foundation for the notion of the quantum coherent state of the electrostatic field of a static external charge distribution introduced in a 1998 paper and rederive formulae
Perturbative versus non-perturbative quantum field theory: the method of Tao, the Casimir effect and interacting Wightman theories
We dwell upon certain points concerning the meaning of quantum field theory: the problems with the perturbative approach, and the question raised by ’t Hooft of the existence of the theory in a
Perturbative versus Non-Perturbative Quantum Field Theory: Tao’s Method, the Casimir Effect, and Interacting Wightman Theories
We dwell upon certain points concerning the meaning of quantum field theory: the problems with the perturbative approach, and the question raised by ’t Hooft of the existence of the theory in a
Static charges and emergence of gauge fields
A universal C*-algebra of gauge invariant operators is presented, describing the electromagnetic field as well as operations creating pairs of static electric charges having opposite signs. Making
The universal algebra of the electromagnetic field III. Static charges and emergence of gauge fields
A universal C*-algebra of gauge invariant operators is presented, describing the electromagnetic field as well as operations creating pairs of static electric charges having opposite signs. Making
Almost Radial Gauge
  • A. Herdegen
  • Mathematics, Physics
    Annales Henri Poincaré
  • 2022
An almost radial gauge $$A^\mathrm {ar}$$ A ar of the electromagnetic potential is constructed for which $$x\cdot A^\mathrm {ar}(x)$$ x · A ar ( x ) vanishes arbitrarily
Asymptotic charges, large gauge transformations and inequivalence of different gauges in external current QED
Abstract In this paper we consider external current QED in the Coulomb gauge and in axial gauges for various spatial directions of the axis. For a non-zero electric charge of the current, we
Asymptotic charges , large gauge transformations and inequivalence of different gauges in external current QED
In this paper we consider external current QED in the Coulomb gauge and in axial gauges for various spatial directions of the axis. For a non-zero electric charge of the current, we demonstrate that
Symplectic reduction of Yang-Mills theory with boundaries: from superselection sectors to edge modes, and back
I develop a theory of symplectic reduction that applies to bounded regions in Yang-Mills theory and electromagnetism. In this theory superselection sectors for the electric-flux play a central role.
Renormalization in String-Localized Field Theories: A Microlocal Analysis
Using methods of microlocal analysis, we prove that the regularization of divergent amplitudes stays a pure ultraviolet problem in string-localized field theories, despite the weaker localization.
...
...

References

SHOWING 1-10 OF 42 REFERENCES
Charges and generators of symmetry transformations in quantum field theory
Within the Wightman approach to quantum field theory, we review and clarify the properties of formal charges, defined as space integrals for the fourth component of a local current. The conditions
Some remarks on local operators in quantum electrodynamics
We assume the existence of a conserved current which generates locally gauge transformations of first kind. We are working in a local quantum Field Theory, where the fields are defined on a vector
On string-localized potentials and gauge fields
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
New Light on Infrared Problems: Sectors, Statistics, Symmetries and Spectrum
A new approach to the analysis of the physical state space of a theory is presented within the general setting of local quantum physics. It also covers theories with long range forces, such as
Locality and the structure of particle states
Starting from the principle of locality of observables we derive localization properties of massive particle states which hold in all models of relativistic quantum theory, including gauge theories.
String-Localized Quantum Fields and Modular Localization
We study free, covariant, quantum (Bose) fields that are associated with irreducible representations of the Poincaré group and localized in semi-infinite strings extending to spacelike infinity.
The role of positivity and causality in interactions involving higher spin
String Chopping and Time-ordered Products of Linear String-localized Quantum Fields
TLDR
This paper shows that almost all such string configurations can be dissected into finitely many pieces which can indeed be chronologically ordered, and fixes the time-ordered products of linear field factors outside a nullset of string configurations.
...
...