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 T^μν mean values and the vacuum energy of the free field vanishes: 0T⁰⁰0 = 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 numbers: 04.62.+v, 02.20.Qs, 98.80.Jk

Print publication: Issue 1 (7 January 2005)
Received 18 May 2004, in final form 28 October 2004
Published 8 December 2004