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Journal of physics A: mathematical and general 38 (2005) 245-256
Krein space quantization in curved and flat spacetimes
T. Garidi1, 2, E. Huguet1, 3, J. Renaud1, 2

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 $T^{\muν}$ mean values and the vacuum energy of the free field vanishes: $\left\langle0\mid T^{00}\mid0\right\rangle$ = 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.
1 :  APC - UMR 7164 - AstroParticule et Cosmologie
2 :  LPTMC - Laboratoire de Physique Théorique de la Matière Condensée
3 :  GEPI - Galaxies, Etoiles, Physique, Instrumentation
Physique/Physique mathématique

Mathématiques/Physique mathématique
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