Volume elements of spacetime and a quartet of scalar fields

Abstract

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 σ. 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 σas 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.

7 pages RevTEX, submitted to Phys. Rev. D

References in corpus (4)

• Cosmology and the Fate of Dilatation Symmetry
• Metric-Affine Gauge Theory of Gravity I. Fundamental Structure and Field Equations
• Gravitational theory without the cosmological constant problem, symmetries of space-filling branes and higher dimensions
• Colliding waves in metric-affine gravity

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