Boundary Quantum Field Theory on the Interior of the Lorentz Hyperboloid

Roberto Longo, Karl-Henning Rehren
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.
open access link Commun. Math. Phys. 311 (2012) 769-785
@article{Longo:2011if, author = "Longo, Roberto and Rehren, Karl-Henning", title = "{Boundary Quantum Field Theory on the Interior of the Lorentz Hyperboloid}", journal = "Commun. Math. Phys.", volume = "311", year = "2012", pages = "769-785", doi = "10.1007/s00220-011-1381-z", eprint = "1103.1141", archivePrefix = "arXiv", primaryClass = "math-ph", SLACcitation = "%%CITATION = ARXIV:1103.1141;%%" }

Keywords: 
algebraic quantum field theory