We construct local, boost covariant boundary QFT nets of von Neumann algebras on the interior of the Lorentz hyperboloid , 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 R, 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 . By considering different states, we shall also have nets in a ground state, rather than in a KMS state.

Longo, R., Rehren, K. (2011). Boundary Quantum Field Theory on the Interior of the Lorentz Hyperboloid. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 311(3), 769-785 [10.1007/s00220-011-1381-z].

Boundary Quantum Field Theory on the Interior of the Lorentz Hyperboloid

LONGO, ROBERTO;
2011-01-01

Abstract

We construct local, boost covariant boundary QFT nets of von Neumann algebras on the interior of the Lorentz hyperboloid , 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 R, 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 . By considering different states, we shall also have nets in a ground state, rather than in a KMS state.
2011
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - ANALISI MATEMATICA
English
Con Impact Factor ISI
Operator Algebras, Quantum Field Theory, Mathematical Physics
Longo, R., Rehren, K. (2011). Boundary Quantum Field Theory on the Interior of the Lorentz Hyperboloid. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 311(3), 769-785 [10.1007/s00220-011-1381-z].
Longo, R; Rehren, K
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/41740
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