The art of the state

TL;DR

This paper reviews a no-go theorem showing the impossibility of defining a preferred vacuum state in quantum field theory on curved spacetimes, and discusses the limitations of proposed geometric states and modifications to achieve Hadamard states.

Contribution

It presents a model-independent no-go theorem for preferred states and introduces a modified construction for Hadamard states based on geometric criteria.

Findings

No universal preferred vacuum state exists in curved spacetime QFT.

Proposed SJ states generally fail to be Hadamard.

A modified construction can produce an infinite family of Hadamard states.

Abstract

Quantum field theory on curved spacetimes lacks an obvious distinguished vacuum state. We review a recent no-go theorem that establishes the impossibility of finding a preferred state in each globally hyperbolic spacetime, subject to certain natural conditions. The result applies in particular to the free scalar field, but the proof is model-independent and therefore of wider applicability. In addition, we critically examine the recently proposed "SJ states", that are determined by the spacetime geometry alone, but which fail to be Hadamard in general. We describe a modified construction that can yield an infinite family of Hadamard states, and also explain recent results that motivate the Hadamard condition without direct reference to ultra-high energies or ultra-short distance structure.