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

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.

First version of March 8, 2014 replaced on Nov 10, 2014

article file
Keywords:

modular localization, string localized quantum fields, renormalization of s=1 couplings in a Hilbert space setting