Asymptotic Observables in Gapped Quantum Spin Systems

Abstract

Abstract. This paper gives a construction of certain asymptotic observables (Araki-Haag detectors) in ground state representations of gapped quantum spin systems. The construction is based on general assumptions which are satisfied e.g. in the Ising model in strong transverse magnetic fields. We do not use the method of propagation estimates, but exploit instead compactness of the relevant propagation observables at any fixed time. Implications for the problem of asymptotic completeness are briefly discussed.

Dressed infrared quantum information

“…What would be much better would be to use a dressed LSZ reduction formula to understand the asymptotic limits of electron correlation functions. [9,17] Nevertheless, the basic physical picture seems clear: in a scattering experiment, one does not measure an electron plus a finely-tuned shockwave of outgoing bremsstrahlung photons, just the electron on its own. This is responsible for well-measured phenomena like radiation damping.…”

“…QED has a complicated asymptotic Hilbert space structure which is still somewhat poorly understood. For example, although Faddeev-Kulish try to define a single, separable Hilbert space H as [8,17] other authors have argued that one needs an uncountable set of separable Hilbert spaces. [7,9] Formally, this is related to the fact that the dressing operator (3) does not converge on the usual Fock space.…”