An Algebraic Construction of Boundary Quantum Field Theory

作者：Longo Roberto^*; Witten Edward

来源：Communications in Mathematical Physics, 2011, 303(1): 213-232.

DOI：10.1007/s00220-010-1133-5

We build up local, time translation covariant Boundary Quantum Field Theory nets of von Neumann algebras on the Minkowski half-plane M (+) starting with a local conformal net of von Neumann algebras on and an element V of a unitary semigroup associated with. The case V = 1 reduces to the net considered by Rehren and one of the authors; if the vacuum character of is summable, is locally isomorphic to. We discuss the structure of the semigroup. 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.
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 further family of models comes from the Ising model.

• 出版日期2011-4