Quantum Field Theory In Curved Spacetime: Quant... [ FULL - 2024 ]

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

. 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

: Because global constructs like Fourier transforms are unavailable, QFTCS must be formulated locally using quantum field operators rather than particle counts. 2. Mathematical Framework: Bogoliubov Transformations Quantum Field Theory in Curved Spacetime: Quant...

: A second observer might decompose the same field using a different basis and operators Mixing : The new annihilation operator

is a linear combination of both the old annihilation and creation operators: Quantum Field Theory in Curved Spacetime: Quantized Fields

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

This framework predicts several landmark effects that bridge the gap between thermodynamics, gravity, and quantum mechanics: The Fundamental Shift: From Particles to Fields :

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 (