Classical and quantum equivalence principle in terms of the path group

Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology

Scientific paper

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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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