Quantum Field Theory In Curved Spacetime: Quant... Now

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 (

Quantum Field Theory in Curved Spacetime: Quantized Fields and Semiclassical Gravity Quantum Field Theory in Curved Spacetime: Quant...

In flat (Minkowski) spacetime, Poincaré invariance provides a unique vacuum state and a global definition of "particles". In curved spacetime, these "crutches" disappear: bj=∑i(αjiai+βji*ai†)b sub j equals sum over i of

: General curved backgrounds lack global Poincaré invariance and time-translation symmetry, making it impossible to define a unique, preferred vacuum state. preferred vacuum state.