, Volume 35, Issue 4, pp 377-434
Date: 09 May 2011

Pascual Jordan’s legacy and the ongoing research in quantum field theory⋆

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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.

Dedicated to my teacher and role model: Rudolf Haag.