# Hadamard states for a scalar field in anti-de Sitter spacetime with arbitrary boundary conditions

@article{Dappiaggi2016HadamardSF, title={Hadamard states for a scalar field in anti-de Sitter spacetime with arbitrary boundary conditions}, author={Claudio Dappiaggi and Hugo R. C. Ferreira}, journal={Physical Review D}, year={2016}, volume={94}, pages={125016} }

We consider a real, massive scalar field on ${\rm PAdS}_{d+1}$, the Poincar\'e domain of the $(d+1)$-dimensional anti-de Sitter (AdS) spacetime. We first determine all admissible boundary conditions that can be applied on the conformal boundary, noting that there exist instances where "bound states" solutions are present. Then, we address the problem of constructing the two-point function for the ground state satisfying those boundary conditions, finding ultimately an explicit closed form. In… Expand

#### 29 Citations

Comment on “Hadamard states for a scalar field in anti–de Sitter spacetime with arbitrary boundary conditions”

- Physics
- Physical Review D
- 2019

In a recent paper (Phys. Rev. D 94, 125016 (2016)), the authors argued that the singularities of the two-point functions on the Poincare domain of the $n$-dimensional anti-de Sitter spacetime… Expand

Ground states of a Klein-Gordon field with Robin boundary conditions in global anti–de Sitter spacetime

- Physics, Mathematics
- 2018

We consider a real, massive scalar field both on the $n$-dimensional anti--de Sitter (AdS$_n$) spacetime and on its universal cover CAdS$_n$. In the second scenario, we extend the recent analysis on… Expand

Boundary conditions and vacuum fluctuations in $${\mathrm {AdS}}_4$$

- Physics
- 2020

Initial conditions given on a spacelike, static slice of a non-globally hyperbolic spacetime may not define the fates of classical and quantum fields uniquely. Such lack of global hyperbolicity is a… Expand

Fundamental solutions and Hadamard states for a scalar field with arbitrary boundary conditions on an asymptotically AdS spacetimes

- Physics, Mathematics
- Mathematical Physics, Analysis and Geometry
- 2021

We consider the Klein-Gordon operator on an n-dimensional asymptotically anti-de Sitter spacetime (M,g) together with arbitrary boundary conditions encoded by a self-adjoint pseudodifferential… Expand

The holographic Hadamard condition on asymptotically anti-de Sitter spacetimes

- Mathematics, Physics
- 2016

In the setting of asymptotically anti-de Sitter spacetimes, we consider Klein–Gordon fields subject to Dirichlet boundary conditions, with mass satisfying the Breitenlohner–Freedman bound. We… Expand

Mode solutions for a Klein-Gordon field in anti-de Sitter spacetime with dynamical boundary conditions of Wentzell type

- Physics, Mathematics
- 2018

We study a real, massive Klein-Gordon field in the Poincare fundamental domain of the (d+1)-dimensional anti–de Sitter (AdS) spacetime, subject to a particular choice of dynamical boundary conditions… Expand

Ground state for a massive scalar field in the BTZ spacetime with Robin boundary conditions

- Physics, Mathematics
- 2017

We consider a real, massive scalar field in BTZ spacetime, a 2+1-dimensional black hole solution of the Einstein's field equations with a negative cosmological constant. First, we analyze the space… Expand

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

- Physics, Mathematics
- 2017

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… Expand

Particle production between isometric frames on a Poincaré patch of AdS2

- Physics
- Journal of Mathematical Physics
- 2019

In a recent paper [J. P. M. Pitelli, Phys. Rev. D {\bf 99}, 108701 (2019)], one of us showed that the vacuum state associated to conformal fields on a Poicare patch of anti-de Sitter spacetime is not… Expand

Aspects of (quantum) field theory on curved spacetimes, particularly in the presence of boundaries

- Mathematics
- 2015

This thesis has two main themes: on the one hand, in Chapters 3 and 5 we study some effects of the presence of timelike boundaries on linear classical and quantum field theories; the second theme is… Expand

#### References

SHOWING 1-10 OF 35 REFERENCES

Quantum scalar field theory on anti-de Sitter space

- Physics
- 2013

This thesis considers a real massive free quantum scalar field propagating with arbitrary coupling to $n$-dimensional anti-de Sitter space.
Analytical expressions are found for the field modes and… Expand

The Large Scale Structure of Space-Time

- Physics, Computer Science
- 1973

The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions. Expand

On Eigenfunction Expansions.

- Mathematics, Medicine
- Proceedings of the National Academy of Sciences of the United States of America
- 1953

The problem of eigenfunction expansion may be formulated as follows: Do there exist functions s,(x, y, y) defined on I X ) and measures m,(E), defined on C such that if one puts for every f(x) E, then there is a function E e @ a projection P( E) of & such that the mapping E -P(E) is a a-Boolean algebra homomorphism. Expand

Gauge/Gravity Duality: Foundations and Applications

- Physics
- 2015

Gauge/gravity duality creates new links between quantum theory and gravity. It has led to new concepts in mathematics and physics, and provides new tools to solve problems in many areas of… Expand

Sturm-Liouville theory

- Mathematics
- 2005

In 1836-1837 Sturm and Liouville published a series of papers on second order linear ordinary differential operators, which started the subject now known as the Sturm-Liouville problem. In 1910… Expand

Advances in Algebraic Quantum Field Theory

- Physics
- 2015

Structural aspects of quantum field theory.- Introduction to Algebraic Quantum Field Theory.- Algebraic Quantum Field Theory on curved backgrounds.- QED and infrared sectors.- Applicative aspects of… Expand

MATH

- 1992

Abstract: About a decade ago, biophysicists observed an approximately linear relationship between the combinatorial complexity of knotted DNA and the distance traveled in gel electrophoresis… Expand

NIST Handbook of Mathematical Functions

- Mathematics, Computer Science
- 2010

This handbook results from a 10-year project conducted by the National Institute of Standards and Technology with an international group of expert authors and validators and is destined to replace its predecessor, the classic but long-outdated Handbook of Mathematical Functions, edited by Abramowitz and Stegun. Expand

A Table of Integrals

- Computer Science
- 2010

Basic Forms x n dx = 1 n + 1 x n+1 (1) 1 x dx = ln |x| (2) udv = uv − vdu (3) 1 ax + b dx = 1 a ln |ax + b| (4) Integrals of Rational Functions 1 (x + a) 2 dx = −

Phys

- Rev. D 78, 044025
- 2008