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 is used for that purpose, with as the components of the metric, we point out other possibilities, namely σ 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.
- Received 16 December 1997
DOI:https://doi.org/10.1103/PhysRevD.58.084021
©1998 American Physical Society