The problem of positivity in 1+1 dimensions and Krein spaces

TL;DR

This paper investigates how Krein spaces can be used to define a positive metric for the massless scalar field in 1+1 dimensions, comparing two realizations and analyzing their properties and advantages.

Contribution

It demonstrates that one Krein space realization of the massless scalar field is a special case of another, providing insights into their differences and benefits.

Findings

One realization is a special case of the other

Both realizations have distinct advantages

Krein spaces can facilitate positive metrics in 1+1D scalar fields

Abstract

The possibility of introducing a positive metric on the states of the massless scalar field in 1+1 dimensions by mean of Krein spaces is examined. Two different realisations in Krein spaces for the massless scalar field are compared. It is proved that one is a particular case of the other. The peculiarities and advantages of both realisations are discussed.