# Local causal structures, Hadamard states and the principle of local covariance in quantum field theory - High Energy Physics - Theory

Local causal structures, Hadamard states and the principle of local covariance in quantum field theory - High Energy Physics - Theory - Download this document for free, or read online. Document in PDF available to download.

Abstract: In the framework of the algebraic formulation, we discuss and analyse somenew features of the local structure of a real scalar quantum field theory in astrongly causal spacetime. In particular we use the properties of theexponential map to set up a local version of a bulk-to-boundary correspondence.The bulk is a suitable subset of a geodesic neighbourhood of any but fixedpoint p of the underlying background, while the boundary is a part of thefuture light cone having p as its own tip. In this regime, we provide a novelnotion for the extended *-algebra of Wick polynomials on the said cone and, onthe one hand, we prove that it contains the information of the bulk counterpartvia an injective *-homomorphism while, on the other hand, we associate to it adistinguished state whose pull-back in the bulk is of Hadamard form. The mainadvantage of this point of view arises if one uses the universal properties ofthe exponential map and of the light cone in order to show that, for any twogiven backgrounds M and M- and for any two subsets of geodesic neighbourhoodsof two arbitrary points, it is possible to engineer the above procedure suchthat the boundary extended algebras are related via a restriction homomorphism.This allows for the pull-back of boundary states in both spacetimes and, thus,to set up a machinery which permits the comparison of expectation values oflocal field observables in M and M-.

Author: ** Claudio Dappiaggi, Nicola Pinamonti, Martin Porrmann**

Source: https://arxiv.org/