Kovariante Quantisierung skalarer Felder im Gravitationsfeld

TLDR: In this paper, a generalized covariant quantization of scalar field operators in a given Gravitational Field is presented, where the equations are picture covariant, that is they have the same form in each picture, especially in the Heisenberg and Schrodinger picture.

Abstract: Zur Ankopplung der Gravitation an die Quantenfeldtheorie werden ortsabhangige unitare Transformationen betrachtet und Ableitungen eingefuhrt, die eine nichtintegrale Transportvorschrift fur Hilbertraumzustande implizieren. Die mit den verallgemeinerten kovarianten Ableitungen gebildete Klein-Gordon-Gleichung fur skalare Feldoperatoren last sich dadurch im vorgegebenen Gravitationsfeld in gleicher Weise wie die Klein-Gordon-Gleichung im Minkowski-Raum quantisieren; die Zustandsvektoren werden wegabhangig. Die Gleichungen sind bildkovariant, d. h. sie haben in jedem Bild dieselbe ausere Gestalt, speziell im Heisenberg und Schrodingerbild. Covariant Quantization of Scalar Fields in a Given Gravitational Field In coupling gravity with the quantum field theory, unitary transformations, depending on space-time-points, are considered and derivatives are introduced, which imply a nonintegrable transport for the state vectors of Hilbert space. The Klein-Gordon-equation, built for scalar field operators with these generalized covariant derivatives, can be quantized now in the same manner in a given gravitational field as the Klein-Gordon-equation in Minkowski space. The quantum state vectors become path dependend. The equations are picture covariant, that is they have the same form in each picture, especially in the Heisenberg picture and the Schrodinger picture.