To relate the perspectives of different observers or the state of fields at different times in an expanding universe, physicists use : Field Decomposition : A scalar field is expanded into a set of basis modes with creation and annihilation operators
In flat (Minkowski) spacetime, Poincaré invariance provides a unique vacuum state and a global definition of "particles". In curved spacetime, these "crutches" disappear: Quantum Field Theory in Curved Spacetime: Quant...
: 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 To relate the perspectives of different observers or