Pascual Jordan's legacy and the ongoing research in quantum field theory
Bert Schroer
October 21, 2010
Pascual Jordan's path-breaking role as the protagonist of quantum field
theory (QFT) is recalled and his friendly dispute with Dirac's particle-based
relativistic quantum theory is presented as the start of the field-particle
conundrum which, though in modified form, persists up to this date. Jordan had
an intuitive understanding that the existence of a causal propagation with
finite propagation speed in a quantum theory led to radically different
physical phenomena than those of QM. The conceptional-mathematical
understanding for such an approach began to emerge only 30 years later. The
strongest link between Jordan's view of QFT and modern "local quantum physics"
is the central role of causal locality as the defining principle of QFT as
opposed to the Born localization in QM. The issue of causal localization is
also the arena where misunderstandings led to a serious derailment of large
part of particle theory e.g. the misinterpretation of an infinite component
pointlike field resulting from the quantization of the Nambu-Goto Lagrangian as
a spacetime quantum string. The new concept of modular localization, which
replaces Jordan's causal locality, is especially important to overcome the
imperfections of gauge theories for which Jordan was the first to note nonlocal
aspects of physical (not Lagrangian) charged fields. Two interesting subjects
in which Jordan was far ahead of his contemporaries will be presented in two
separate sections.
Keywords:
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