Abstract
The goal of this chapter is twofold. On the one hand we will review how the algebra of observables for a real scalar field on globally hyperbolic spacetimes is built. We will show in addition that a similar construction exists when one consider a suitable class of null manifolds of which future and past null infinity, discussed in the previous chapter, are the prototypes.
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Notes
- 1.
In the rest of the book \(P G^\pm \) and \(G^\pm P\) and other similar expressions are understood as compositions of linear operators omitting, as is usual for linear operators, the composition symbol \(\circ \).
- 2.
As far as the analysis in this section is concerned, one could more generally consider a d-sphere in place of \(\mathbb {S}^2\) and all the results would still be valid. We avoid such degree of generality to make more manifest the connection with the preceding chapter.
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Dappiaggi, C., Moretti, V., Pinamonti, N. (2017). Quantum Fields in Spacetimes with Null Surfaces. In: Hadamard States from Light-like Hypersurfaces. SpringerBriefs in Mathematical Physics, vol 25. Springer, Cham. https://doi.org/10.1007/978-3-319-64343-4_3
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