Quantum fields in curved space-times

Abstract

The problem of obtaining a quantum description of the (real) KleinGordon system in a given curved space-time is discussed. An algebraic approach is used. The *-algebra of quantum operators is constructed explicitly and the problem of finding its *-representation is reduced to th at of selecting a suitable complex structure on the real vector space of the solutions of the (classical) Klein-Gordon equation. Since, in a static space-time, there already exists, a satisfactory quantum field theory, in this case one already knows what the ‘ correct ’ complex structure is. A physical characterization of this * correct ’ complex structure is obtained. This characterization is used to extend quantum field theory to nonstatic space-times. Stationary space-times are considered first. In this case, the issue of extension is completely straightforward and the resulting theory is the natural generalization of the one in static space-times. General, non-stationary space-times are then considered. In this case the issue of extension is quite complicated and we only present a plausible extension. Although the resulting framework is well-defined mathematically, the physical interpretation associated with it is rather unconventional. Merits and weaknesses of this framework are discussed.