Hadamard states from null infinity

Claudio Dappiaggi
January 20, 2015
Free field theories on a four dimensional, globally hyperbolic spacetime, whose dynamics is ruled by a Green hyperbolic partial differential operator, can be quantized following the algebraic approach. It consists of a two-step procedure: In the first part one identifies the observables of the underlying physical system collecting them in a *-algebra which encodes their relational and structural properties. In the second step one must identify a quantum state, that is a positive, normalized linear functional on the *-algebra out of which one recovers the interpretation proper of quantum mechanical theories via the so-called Gelfand-Naimark-Segal theorem. In between the plethora of possible states, only few of them are considered physically acceptable and they are all characterized by the so-called Hadamard condition, a constraint on the singular structure of the associated two-point function. Goal of this paper is to outline a construction scheme for these states which can be applied whenever the underlying background possesses a null (conformal) boundary. We discuss in particular the examples of a real, massless conformally coupled scalar field and of linearized gravity on a globally hyperbolic and asymptotically flat spacetime.
open access link
@inproceedings{Dappiaggi:2015asa, author = "Dappiaggi, Claudio", title = "{Hadamard states from null infinity}", url = "http://inspirehep.net/record/1340300/files/arXiv:1501.04808.pdf", year = "2015", eprint = "1501.04808", archivePrefix = "arXiv", primaryClass = "math-ph", SLACcitation = "%%CITATION = ARXIV:1501.04808;%%" }

Keywords: 
quantum field theory on curved spacetimes, Hadamard states