# On the algebraic quantization of a massive scalar field in anti-de-Sitter spacetime

## TL;DR

This paper develops an algebraic framework for quantizing a massive scalar field in anti-de Sitter spacetime, establishing properties of the observable algebra and extending the concept of Hadamard states.

## Contribution

It introduces a method to associate a causality-respecting algebra of observables for scalar fields in AdS with arbitrary boundary conditions, generalizing Hadamard states.

## Key findings

- Established algebraic properties like causality and the time-slice axiom.
- Characterized the wavefront set of the ground state.
- Constructed a global algebra of Wick polynomials.

## Abstract

We discuss the algebraic quantization of a real, massive scalar field in the Poincar\'e patch of the (d+1)-dimensional anti-de Sitter spacetime, with arbitrary boundary conditions. By using the functional formalism, we show that it is always possible to associate to such system an algebra of observables enjoying the standard properties of causality, time-slice axiom and F-locality. In addition, we characterize the wavefront set of the ground state associated to the system under investigation. As a consequence, we are able to generalize the definition of Hadamard states and construct a global algebra of Wick polynomials.