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

: The concept of a "particle" becomes local and observer-dependent. Different observers (e.g., one inertial and one accelerating) may disagree on whether a state contains particles or is a vacuum.

: In the early, rapidly expanding universe, time-varying gravitational fields can "excite" the vacuum, creating elementary particles that seed the large-scale structure of the universe. Robert Wald - Quantum Field Theory in Curved Spacetime Quantum Field Theory in Curved Spacetime: Quant...

Quantum Field Theory in Curved Spacetime (QFTCS) is a "hybrid" framework where matter fields are treated according to quantum principles, but the gravitational background is described classically by a fixed spacetime metric gμνg sub mu nu end-sub : The concept of a "particle" becomes local

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 ( Robert Wald - Quantum Field Theory in Curved

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

: 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