1992
DOI: 10.1142/s0129055x92000170
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Superselection Sectors With Braid Group Statistics and Exchange Algebras Ii: Geometric Aspects and Conformal Covariance

Abstract: The general theory of superselection sectors is shown to provide almost all the structure observed in two-dimensional conformal field theories. Its application to two-dimensional conformally covariant and three-dimensional Poincaré covariant theories yields a general spin-statistics connection previously encountered in more special situations. CPT symmetry can be shown also in the absence of local (anti-) commutation relations, if the braid group statistics is expressed in the form of an exchange algebra.

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Cited by 133 publications
(196 citation statements)
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“…(15) below). To realize such statistics, the fields which create a charge localized in a given space-like cone C need an additional information: Namely, a path in the set of space-like directions H starting from some fixed reference direction e 0 and "ending" in C. 4 We shall sketch this concept, which has been introduced in [9], in a slightly modified form introduced in [16]. We say that a space-like cone C contains a space-like direction e if C + e ⊂ C .…”
Section: Framework Assumptions and Resultsmentioning
confidence: 99%
“…(15) below). To realize such statistics, the fields which create a charge localized in a given space-like cone C need an additional information: Namely, a path in the set of space-like directions H starting from some fixed reference direction e 0 and "ending" in C. 4 We shall sketch this concept, which has been introduced in [9], in a slightly modified form introduced in [16]. We say that a space-like cone C contains a space-like direction e if C + e ⊂ C .…”
Section: Framework Assumptions and Resultsmentioning
confidence: 99%
“…It is quite obvious that the braided tensor structure on Rep A provided by the above constructions is independent, up to equivalence, of the choice of the point ∞ ∈ S 1 . For an approach to the representation theory of QFTs on S 1 that does not rely on cutting the circle see [21]. The latter, however, seems less suited for the analysis of G−Loc A for non-trivial G since the g-localized endomorphisms of A ∞ do not extend to endomorphisms of the global algebra A univ of [21] if g = e.…”
Section: Remarkmentioning
confidence: 99%
“…In Section 3 we will mostly be interested in finite groups, but we will also comment on infinite compact groups. ✷ The subsequent considerations are straightforward generalizations of the well known theory [16,20,21] for G = {e}. Since modifications of the latter are needed throughout -and also in the interest of the non-expert reader -we prefer to develop the case for non-trivial G from scratch.…”
mentioning
confidence: 99%
“…All that was done for quantum field theories on Minkowski spacetime in dimensions d ≥ 3. Other groups of researchers have been able to follow the same route in various directions, especially in the direction of conformal quantum field theory in two dimensions, and besides the crucial results of Fredenhagen, Rehren and Schroer [24], the main success was obtained by Kawahigashi and Longo in [34], where they have been able to completely classify theories with central charge less than one.…”
Section: Introductionmentioning
confidence: 99%