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Journal of Physics A: Mathematical and General

Krein space quantization in curved and flat spacetimes

Author

T Garidi 1,2, E Huguet 2,3 and J Renaud 1,2

Affiliations

1 LPTMC, Université Paris 7-Denis Diderot, boite 7020, F-75251 Paris Cedex 05, France
2 Fédération de recherche APC, Université Paris 7-Denis Diderot, boite 7020, F-75251 Paris Cedex 05, France
3 GEPI, Observatoire de Paris, 5 place J. Janssen, 92195 Meudon Cedex, France

E-mail

garidi@kalymnos.unige.ch eric.huguet@obspm.fr renaud@ccr.jussieu.fr

Journal

Journal of Physics A: Mathematical and General Create an alert RSS this journal

Issue

Volume 38, Number 1

Citation

T Garidi et al 2005 J. Phys. A: Math. Gen. 38 245

doi: 10.1088/0305-4470/38/1/018


Article References Cited By
 
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Abstract

We re-examine in detail a canonical quantization method à la Gupta–Bleuler in which the Fock space is built over a so-called Krein space. This method has already been successfully applied to the massless minimally coupled scalar field in de Sitter spacetime for which it preserves covariance. Here, it is formulated in a more general context. An interesting feature of the theory is that, although the field is obtained by canonical quantization, it is independent of Bogoliubov transformations. Moreover, no infinite term appears in the computation of Tμν mean values and the vacuum energy of the free field vanishes: lang0midT00mid0rang = 0. We also investigate the behaviour of the Krein quantization in Minkowski space for a theory with interaction. We show that one can recover the usual theory with the exception that the vacuum energy of the free theory is zero.

 
PACS

04.62.+v Quantum fields in curved spacetime

03.65.Nk Scattering theory

02.40.-k Geometry, differential geometry, and topology

MSC

81T20 Quantum field theory on curved space backgrounds

81U20 S-matrix theory, etc.

83C47 Methods of quantum field theory (See also 81T20)

46C20 Spaces with indefinite inner product (Kreĭn spaces, Pontryagin spaces, etc.) (See also 47B50)

Subjects

Mathematical physics

Gravitation and cosmology

Quantum information and quantum mechanics

Dates

Issue 1 (7 January 2005)

Received 18 May 2004 , in final form 28 October 2004

Published 8 December 2004



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