# Boundary Quantum Field Theory on the Interior of the Lorentz Hyperboloid

March 06, 2011

We construct local, boost covariant boundary QFT nets of von Neumann algebras
on the interior of the Lorentz hyperboloid LH = {x^2 - t^2 > R^2, x>0}, in the
two-dimensional Minkowski spacetime. Our first construction is canonical,
starting with a local conformal net on the real line, and is analogous to our
previous construction of local boundary CFT nets on the Minkowski half-space.
This net is in a thermal state at Hawking temperature. Then, inspired by a
recent construction by E. Witten and one of us, we consider a unitary semigroup
that we use to build up infinitely many nets. Surprisingly, the one-particle
semigroup is again isomorphic to the semigroup of symmetric inner functions of
the disk. In particular, by considering the U(1)-current net, we can associate
with any given symmetric inner function a local, boundary QFT net on LH. By
considering different states, we shall also have nets in a ground state, rather
than in a KMS state.

Keywords:

algebraic quantum field theory