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Noninteraction of Waves in Two-dimensional Conformal Field Theory

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Abstract

In higher dimensional quantum field theory, irreducible representations of the Poincaré group are associated with particles. Their counterpart in two-dimensional massless models are “waves” introduced by Buchholz. In this paper we show that waves do not interact in two-dimensional Möbius covariant theories and in- and out-asymptotic fields coincide. We identify the set of the collision states of waves with the subspace generated by the chiral components of the Möbius covariant net from the vacuum. It is also shown that Bisognano-Wichmann property, dilation covariance and asymptotic completeness (with respect to waves) imply Möbius symmetry.

Under natural assumptions, we observe that the maps which give asymptotic fields in Poincaré covariant theory are conditional expectations between appropriate algebras. We show that a two-dimensional massless theory is asymptotically complete and noninteracting if and only if it is a chiral Möbius covariant theory.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 1, 00133, Roma, Italy

    Yoh Tanimoto

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  1. Yoh Tanimoto
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Correspondence to Yoh Tanimoto.

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Communicated by Y. Kawahigashi

Supported in part by the ERC Advanced Grant 227458 OACFT “Operator Algebras and Conformal Field Theory”.

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Tanimoto, Y. Noninteraction of Waves in Two-dimensional Conformal Field Theory. Commun. Math. Phys. 314, 419–441 (2012). https://doi.org/10.1007/s00220-012-1439-6

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