  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.
