Hagen Kleinert, in his book, Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets, 4 Edition, generalizes the Equivalence principle with what he calls a nonholonomic transformation. He transforms equations in flat space into spaces with curvature and torsion using differential transformtions of the form(adsbygoogle = window.adsbygoogle || []).push({});

[tex]d{x^i} = \frac{{\partial {x^i}}}{{\partial {q^\mu }}}d{q^\mu }[/tex]

where

[tex]{x^i} = {x^i}({q^\mu })[/tex]

and where x is in flat space and q is in curved space. See equations 10.21 and 10.12 in the above link.

My question is whether this is a diffeomorphism as is required by diffeomorphism invariance of general relativity. Do all we need to do is make this differential transformation substitution in order to convert flat space physics to curved space physics? Thanks.

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# Is nonholonomic Xformation = Diffeomorphism

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