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تسجيل مستخدم جديدVolume elements of spacetime and a quartet of scalar fields
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Starting with a `bare 4-dimensional differential manifold as a model of spacetime, we discuss the options one has for defining a volume element which can be used for physical theories. We show that one has to prescribe a scalar density sigma. Whereas conventionally sqrt{|det g_{ij}|} is used for that purpose, with g_{ij} as the components of the metric, we point out other possibilities, namely sigma as a `dilaton field or as a derived quantity from either a linear connection or a quartet of scalar fields, as suggested by Guendelman and Kaganovich.
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