A Critical Look at 50 Years Particle Theory from the Perspective of the Crossing Property

Abstract

The crossing property is perhaps the most subtle aspect of the particlefield relation. Although it is not difficult to state its content in terms of certain analytic properties relating different matrixelements of the S-matrix or formfactors, its relation to the localization-and positive energy spectral principles requires a level of insight into the inner workings of QFT which goes beyond anything which can be found in typical textbooks on QFT. This paper presents a recent account based on new ideas derived from "modular localization" including a mathematic appendix on this subject. Its main achievement is the proof of the crossing property from a two-algebra generalization of the KMS condition.The main content is an in-depth criticism of the dual model and its string theoretic extension. The conceptual flaws of these models are closely related to misunderstandings of crossing. The correct interpretation of string theory is that of a dynamic infinite component one particle space where "dynamic" means that, unlike a mere collection of independent free fields, the formalism contains also operators which communicate between the different irreducible Poincaré representations and set the mass/spin spectrum. Whereas in pre-string times there were unsuccessful attempts to achieve this in analogy to the O(4, 2) hydrogen spectrum by the use of higher noncompact groups, the superstring in d = 9 + 1, which uses instead (bosonic/fermionic) oscillators obtained from multicomponent chiral currents, is the only known solution of the dynamical infinite component pointlike field (or pointlike generated wave function) project. Dedicated to Ivan Todorov on the occasion of his 75th birthday. B. Schroer ( ) CBPF, Rua Dr. Xavier Sigaud 150,

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

“…The KMS relation for interacting fields, from which the particle crossing is to be derived, reads now [54] …”

“…In this way one overcomes the clash between pointlike K-field with the Hilbert space structure [37] [54]. Although for massive pointlike potentials (Proca potentials) a direct clash with the Hilbert space structure does not exist, the problem returns in a more hidden form through the lack of renormalizability of pointlike massive vectormeson interactions.…”

“…As explained in the text, the problem amounts to establish the vanishing of all correlation functions which contain would be physical stringlocal gluon or quark operators in the limit of vanishing vectormeson mass 54 . Using the vectormeson mass m as a natural covariant infrared cutoff and the fact that the m → 0 limes comes with logarithmic divergencies in perturbation theory, this result is very plausible.…”

Jorge A. Swieca’s contributions to quantum field theory in the 60s and 70s and their relevance in present research

“…Indeed the bootstrap program lacked even the means to implement its most celebrated addition to particle theory, the crossing property (which follows from QFT [4]) and, which is a serious flaw, it never addressed those requirements which macro-causality imposes on any multi-particle S-matrix [5]. These properties were first listed by Stueckelberg who also used them to criticize the previously mentioned Heisenberg S-matrix proposal 4 ; they basically consisted in the spacelike cluster factorare composites of a fundamental spinor field), Pauli abruptly (without looking for excuses) abandoned and criticized these attempts after Feynman showed him the fallacies. 3 The arena of the Streitkultur of the 60s and 70s were conferences and was reflected in many conference reports, sometimes even in regular articles [1].…”

“…3 The arena of the Streitkultur of the 60s and 70s were conferences and was reflected in many conference reports, sometimes even in regular articles [1]. 4 The first attempt to bypass QFT and formulate particle physics solely in terms of the Smatrix is due to Heisenberg [6]. He wrote wrote down models of unitary Poincaré-invariant operators.…”