Covariant Schrödinger operator. (English) Zbl 1057.81050

Janyška, Josef; Modugno, Marco

J. Phys. A, Math. Gen. 35, No. 40, 8407-8434 (2002).

Summary: We analyse the Schrödinger operator for a quantum scalar particle in a curved spacetime which is fibred over absolute time and is equipped with given spacelike metric, gravitational field and electromagnetic field. We approach the Schrödinger operator in three independent ways: in terms of covariant differentials induced by the quantum connection, via a quantum Lagrangian and directly by the only requirement of general covariance. In particular, in the flat case, our Schrödinger operator coincides with the standard one.

MSC:

81T20	Quantum field theory on curved space or space-time backgrounds
81R20	Covariant wave equations in quantum theory, relativistic quantum mechanics
58A20	Jets in global analysis
58J90	Applications of PDEs on manifolds
81V17	Gravitational interaction in quantum theory