Krein space quantization in curved and flat spacetimes

TL;DR

This paper explores Krein space quantization in both curved and flat spacetimes, demonstrating its advantages such as covariance preservation, absence of infinite terms, and zero vacuum energy, with implications for quantum field theory.

Contribution

It generalizes Krein space quantization beyond de Sitter space, showing it yields finite, covariant results and zero vacuum energy even with interactions.

Findings

Vacuum energy of free field is zero in Krein quantization.

The method is independent of Bogoliubov transformations.

It recovers standard theory results with modified vacuum energy.

Abstract

We reexamine in detail a canonical quantization method a 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 $T^{\mu\nu}$ mean values and the vacuum energy of the free field vanishes: $<0|T^{00}|0>=0$. 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.