T Garidi et al 2005 J. Phys. A: Math. Gen. 38 245 doi:10.1088/0305-4470/38/1/018
Krein space quantization in curved and flat spacetimes
T Garidi1,2, E Huguet2,3 and J Renaud1,2
Show affiliationsWe 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: 
0
T000
= 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
- MSC
-
81T20 Quantum field theory on curved space backgrounds
83C47 Methods of quantum field theory (See also 81T20)
46C20 Spaces with indefinite inner product (Kreĭn spaces, Pontryagin spaces, etc.) (See also 47B50)
- Subjects
- Dates
-
Issue 1 (7 January 2005)
Received 18 May 2004, in final form 28 October 2004
Published 8 December 2004
-
Krein space quantization in curved and flat spacetimes
T Garidi et al 2005 J. Phys. A: Math. Gen. 38 245
-
Theory of symmetry for a rotational relativistic Birkhoff system
Luo Shao-Kai et al 2002 Chinese Phys. 11 429
-
First-order Dirac symmetry operators
I M Benn and J M Kress 2004 Class. Quantum Grav. 21 427
-
Projected spin networks for Lorentz connection: linking spin foams and loop gravity
Etera R Livine 2002 Class. Quantum Grav. 19 5525
-
A diffuse neutron scattering study of local atomic order and pair interaction potentials in disordered FCC γ-MnNi alloys
O Moze and T J Hicks 1984 J. Phys. F: Met. Phys. 14 211
-
A study of energy and effective atomic number dependence of the exposure build-up factors in biological samples
G S Sidhu et al 2000 J. Radiol. Prot. 20 53
-
Instabilities in an inductively coupled oxygen plasma
C S Corr et al 2003 Plasma Sources Sci. Technol. 12 265
-
A broadband controller for shunt piezoelectric damping of structural vibration
S Behrens et al 2003 Smart Mater. Struct. 12 18
-
Self-organization effects and light amplification of collective atomic recoil motion in a harmonic trap
Lin Zhang et al 2005 J. Opt. B: Quantum Semiclass. Opt. 7 355
-
News from the BIPM—2005
Andrew Wallard 2006 Metrologia 43 175
Related review articles
What's this?- Integrable structure of box–ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry
- The effective temperature
- Spectral problems in open quantum chaos