Volume elements of space-time and a quartet of scalar fields
Dec, 1997
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Abstract: (arXiv)
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.Note:
- 7 pages RevTEX, submitted to Phys. Rev. D
- space-time: measure
- differential geometry
- field theory: scalar
- dilaton
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