Quantum Fields from Causal Order

TL;DR

This thesis explores observer-independent quantum field theory in curved spacetime, focusing on the Sorkin-Johnston vacuum and a spacetime-based entanglement entropy, revealing new insights into quantum fields and entanglement in curved backgrounds.

Contribution

It introduces and analyzes the Sorkin-Johnston vacuum in various curved spacetimes and develops the Sorkin Spacetime Entanglement Entropy, advancing understanding of quantum fields and entanglement in curved spacetime.

Findings

SJ vacuum properties differ from known vacua in specific spacetimes

SSEE matches known entanglement entropy results in certain cases

New insights into quantum fields near horizons and in curved backgrounds

Abstract

We study different aspects of observer independent formulation of quantum field theory (QFT) in curved spacetime background. This thesis is broadly divided into two parts, in the first part we study an observer independent scalar field vacuum, called as the Sorkin-Johnston (SJ) vacuum for a small mass scalar field in a 2d causal diamond, and conformally coupled scalar field in spacetimes which are conformally related to ultrastatic spacetime with time dependent conformal factor. We study several properties of the SJ vacuum in these spacetimes and compare with the known vacua. In the second part of the thesis we study a spacetime formulation of entanglement entropy, called as the Sorkin Spacetime Entanglement Entropy (SSEE), in curved spacetime, which makes use of the Wightman function restricted to the region of interest and the spacetime field commutator. We study SSEE in cylinder slab spacetimes and compare the result with the Calabrese-Cardy entanglement entropy. We also study SSEE of de Sitter and black hole horizons and compared with known results.