Classical and quantum equivalence principle in terms of the path group

Details Classical and quantum equivalence principle in terms of the path group Classical and quantum equivalence principle in terms of the path group

2000-10-28

arxiv.org/abs/gr-qc/0010105v2

Helv.Phys.Acta 69:301-304,1996

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

LATEX, 5 pages

Scientific paper

A natural mapping of paths in a curved space onto the paths in the corresponding (tangent) flat space may be used to reduce the curved-space-time path integral to the flat-space-time path integral. The dynamics of the particle in a curved space-time is expressed then in terms of an integral over paths in the flat (Minkowski) space-time. This may be called quantum equivalence principle. Contrary to the known DeWitt's definition of a curved-space path integral, the present definition leads to the covariant equation of motion without a scalar curvature term. The reduction of a curved-space path integral to the flat-space path integral may be expressed in terms of a representation of the path group. With the help of this representation all the results may be generalized to the case of an arbitrary external field.

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