Modular localization and the holistic structure of causal quantum theory, a historical perspective

Bert Schroer
March 08, 2014
Recent insights into the conceptual structure of localization in QFT ("modular localization") led to clari…cations of old unsolved problems. The oldest one is the Einstein-Jordan conundrum which led Jordan in 1925 to the discovery of quantum …field theory. This comparison of ‡fluctu- ations in subsystems of heat bath systems (Einstein) with those resulting from the restriction of the QFT vacuum state to an open subvolume (Jor- dan) leads to a perfect analogy; the globally pure vacuum state becomes upon local restriction a strongly impure KMS state. This phenomenon of localization-caused thermal behavior as well as the vacuum-polarization clouds at the causal boundary of the localization region places localization in QFT into a sharp contrast with quantum mechanics and justi…fies the attribute "holistic". In fact it positions the E-J Gedankenexperiment into the same conceptual category as the cosmological constant problem and the Unruh Gedankenexperiment. The holistic structure of QFT resulting from "modular localization" also leads to a revision of the conceptual ori- gin of the crucial crossing property which entered particle theory at the time of the bootstrap S-matrix approach but suffered from incorrect use in the S-matrix settings of the dual model and string theory. The new holistic point of view, which strengthens the autonomous aspect of QFT, also comes with new messages for gauge theory by exposing the clash between Hilbert space structure and localization and presenting alternative solutions based on the use of stringlocal …fields in Hilbert space. Among other things this leads to a radical reformulation of the Englert- Higgs symmetry breaking mechanism.
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modular localization, string localized quantum fields, renormalization of s=1 couplings in a Hilbert space setting