Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-11-15
J.Phys.A44:095402,2011
Physics
High Energy Physics
High Energy Physics - Theory
14 pages, no figures, typos corrected
Scientific paper
10.1088/1751-8113/44/9/095402
We discuss the quantum dynamics of a particle in static curved spacetimes in a coordinate representation. The scheme is based on the analysis of the squared energy operator E^2, which is quadratic in momenta and contains a scalar curvature term. Our main emphasis is on AdS spaces, where this term is fixed by the isometry group. As a byproduct the isometry generators are constructed and the energy spectrum is reproduced. In the massless case the conformal symmetry is realized as well. We show the equivalence between this quantization and the covariant quantization, based on the Klein-Gordon type equation in AdS. We further demonstrate that the two quantization methods in an arbitrary (N+1)-dimensional static spacetime are equivalent to each other if the scalar curvature terms both in the operator E^2 and in the Klein-Gordon type equation have the same coefficient equal to (N-1)/(4N).
Dorn Harald
Jorjadze George
Kalousios Chrysostomos
Plefka Jan
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