Über Teilsysteme von $$\bar \Theta $$ ({g})

String-localized quantum fields from Wigner representations

“…Our construction of string-localized fields is based on Tomita-Takeski modular theory (see [15] for a survey of its applications to quantum field theory) in the context of modular localization for Poincaré covariant positive energy representations [7,16,17,18,19]. A full treatment in the modular setting will be given in [20].…”

“…From the modular duality results of [7] it follows that such operators must be contained in the intersection of the operator algebras generated by string field operators localized in wedge domains containing the bounded localization domain, so the question is whether the intersections of the wedge algebras contain nontrivial local operators. A sufficent condition based on nuclearity properties of modular operators has very recently been given in [18] but it is restricted to space-time dimensions not larger than two and hence not applicable in the present case without modifications.…”

“…The concept of modular localization, that inspired the present construction of string localized fields, can be regarded as a modern realization of this vision of Jordan. One of its achievements is the successful derivation, from first principles, of the recipes of the bootstrap-formfactor programs for the rich class of d = 1 + 1 factorising models [17,18]. What has been missing up to now is an example demonstrating beyond doubt that this trans-Lagrangean point of view is also relevant in four space-time dimensions.…”

Rosser provability and the second incompleteness theorem

“…). Therefore the uniform ∆ 0 reflection principle ∀x(∆ 0 (x) ∧ Pr R 1 (x) → True ∆0 (x)) for Pr R 1 (x) is provable in PA. 3 Before proving our results, we introduce some terminology and prove a lemma. We assume that our logical symbols are only ∧, ¬ and ∀, and other logical symbols such as → and ∃ are introduced as abbreviations.…”

“…Other sets of derivability conditions which are sufficient for the second incompleteness theorem have been proposed by Jeroslow [10], Montagna [21] and Buchholz [3] (see also [16]). On the other hand, the second incompleteness theorem does not hold for some provability predicates.…”