The Myth of Coordinate Freedom скачать в хорошем качестве

The Myth of Coordinate Freedom

"Coordinate-free" formulations are not more fundamental. They are compressed notations that conceal coordinates while remaining entirely dependent on them. Fields are functions of spacetime variables. Correlation functions depend on spacetime separation. Renormalization is performed by regulating integrals over momentum or position coordinates. Attempts to construct coordinate-free formulations of QFT inevitably reintroduce coordinates under different names: fiber bundle charts, local trivializations, tetrads, or test functions with compact support. Every scattering amplitude, propagator, and Green function is computed in explicit coordinate form. The abstraction never replaces the coordinates. It merely postpones them.