# Semidirect product of CCR and CAR algebras and asymptotic states in quantum electrodynamics

@article{Herdegen1998SemidirectPO,
title={Semidirect product of CCR and CAR algebras and asymptotic states in quantum electrodynamics},
author={Andrzej Herdegen},
journal={Journal of Mathematical Physics},
year={1998},
volume={39},
pages={1788-1817}
}
• A. Herdegen
• Published 10 November 1997
• Mathematics, Physics
• Journal of Mathematical Physics
A C*-algebra containing the CCR and CAR algebras as its subalgebras and naturally described as the semidirect product of these algebras is discussed. A particular example of this structure is considered as a model for the algebra of asymptotic fields in quantum electrodynamics in which Gauss’ law is respected. The appearance in this algebra of a phase variable related to electromagnetic potential leads to the universal charge quantization. Translationally covariant representations of this…
19 Citations
MASSLESS SCALAR FREE FIELD IN 1+1 DIMENSIONS I: WEYL ALGEBRAS PRODUCTS AND SUPERSELECTION SECTORS
This is the first of two papers on the superselection sectors of the conformal model in the title, in a time zero formulation. A classification of the sectors of the net of observables as
Massless Asymptotic Fields and Haag–Ruelle Theory
• Mathematics, Physics
• 2014
We revisit the problem of the existence of asymptotic massless boson fields in quantum field theory. The well-known construction of such fields by Buchholz (Commun. Math. Phys. 52:147–173, 1977;
• 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
Infrared Finite Scattering Theory in Quantum Field Theory and Quantum Gravity
• Physics
• 2022
earliest of quantum ﬁeld theory (QFT) that infrared divergences arise in scattering theory with massless ﬁelds. These infrared divergences are manifestations of the memory eﬀect: At order 1 /r a
Asymptotic symmetries in the BV-BFV formalism. (English)
• Mathematics
• 2022
A classical field theory on a manifold with boundary phrased in the BV-BFV formalism is described by two sets of data, one assigned to the bulk manifold and one to the boundary, together with an
Infrared problem in perturbative quantum field theory
• P. Duch
• Physics
Reviews in Mathematical Physics
• 2021
We propose a mathematically rigorous construction of the scattering matrix and the interacting fields in models of relativistic perturbative quantum field theory with massless fields and long-range
Foundations of quantum physics V . Coherent foundations Arnold Neumaier
This paper is a programmatic article presenting an outline of a new view of the foundations of quantum mechanics and quantum field theory. In short, the proposed foundations are given by the
Spacelike Localization of Long-Range Fields in a Model of Asymptotic Electrodynamics
• Mathematics, Physics
• 2011
A previously proposed algebra of asymptotic fields in quantum electrodynamics is formulated as a net of algebras localized in regions which in general have unbounded spacelike extension.
Foundations of quantum physics V. Coherent foundations
This paper is a programmatic article presenting an outline of a new view of the foundations of quantum mechanics and quantum field theory. In short, the proposed foundations are given by the
Rigorous construction and Hadamard property of the Unruh state in Schwarzschild spacetime
• Physics
• 2009
The discovery of the radiation properties of black holes prompted the search for a natural candidate quantum ground state for a massless scalar field theory on Schwarzschild spacetime, here

## References

SHOWING 1-10 OF 52 REFERENCES
Twisted crossed products of C*-algebras
• Mathematics
Mathematical Proceedings of the Cambridge Philosophical Society
• 1989
Group algebras and crossed products have always played an important role in the theory of C*-algebras, and there has also been considerable interest in various twisted analogues, where the
Asymptotic algebra for charged particles and radiation
A C*‐algebra of asymptotic fields which properly describes the infrared structure in quantum electrodynamics is proposed. The algebra is generated by the null asymptotic of electromagnetic field and
Physical states in quantum electrodynamics
Because of difficulties with the Gupta-Bleuler subsidiary condition in the charged sectors, an alternative scheme for identifying physical states in the indefinite-metric space I of quantum
The physical state space of quantum electrodynamics
Starting from the fact that electrically charged particles are massive, we derive a criterion which characterizes the state space of quantum electrodynamics. This criterion clarifies the special role
Quasi-free states of the C.C.R.—Algebra and Bogoliubov transformations
• Mathematics
• 1968
We give a complete characterization of quasi-free states (generalized free states) of the C.C.R. algebra. We prove that the pure quasi-free states areall Fock states and that any two Fock states are
The smallestC*-algebra for canonical commutations relations
• Mathematics
• 1973
We consider theC*-algebras which contain the Weyl operators when the symplectic form which defines the C.C.R. is possibly degenerate. We prove that the C.C.R. are all obtained as a quotient of a
Asymptotic Structure of Space-Time
Many physical theories have the feature that one can distinguish within the theory a certain class of models which one regards as representing “isolated systems”. In Newtonian gravitation, to take
The Maxwell-Dirac equations: Asymptotic completeness and the infrared problem
• Mathematics
• 1994
In this article we present an announcement of results concerning: a) A solution to the Cauchy problem for the M-D equations, namely global existence, for small initial data at t = 0, of solutions for