Quantum Field Theory In Curved Spacetime: Quant... May 2026

bj=∑i(αjiai+βji*ai†)b sub j equals sum over i of open paren alpha sub j i end-sub a sub i plus beta sub j i end-sub raised to the * power a sub i raised to the † power close paren If the "mixing coefficient" βjibeta sub j i end-sub is non-zero, the vacuum of the first observer (

. This approach serves as a robust approximation for environments where gravity is strong but quantum gravitational effects—such as fluctuations of the metric itself—are not yet dominant. 1. The Fundamental Shift: From Particles to Fields Quantum Field Theory in Curved Spacetime: Quant...

is a linear combination of both the old annihilation and creation operators: bj=∑i(αjiai+βji*ai†)b sub j equals sum over i of

Quantum Field Theory in Curved Spacetime: Quantized Fields and Semiclassical Gravity The Fundamental Shift: From Particles to Fields is

In flat (Minkowski) spacetime, Poincaré invariance provides a unique vacuum state and a global definition of "particles". In curved spacetime, these "crutches" disappear: