An Algebraic Construction of Boundary Quantum Field Theory

Roberto Longo, Edward Witten

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


We build up local, time translation covariant Boundary Quantum Field Theory nets of von Neumann algebras Av on the Minkowski half-plane M+ starting with a local conformal net of von Neumann algebras on ℝ and an element V of a unitary semigroup ε(A) associated with A. The case V = 1 reduces to the net A+ considered by Rehren and one of the authors; if the vacuum character of A is summable, A+ is locally isomorphic to ε(A). We discuss the structure of the semigroup ε(A). By using a one-particle version of Borchers theorem and standard subspace analysis, we provide an abstract analog of the Beurling-Lax theorem that allows us to describe, in particular, all unitaries on the one-particle Hilbert space whose second quantization promotion belongs to ε(A(0)) with A(0) the U(1)-current net. Each such unitary is attached to a scattering function or, more generally, to a symmetric inner function. We then obtain families of models via any Buchholz-Mack-Todorov extension of A(0). A further family of models comes from the Ising model.

Original languageEnglish (US)
Pages (from-to)213-232
Number of pages20
JournalCommunications In Mathematical Physics
Issue number1
StatePublished - Apr 2011
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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