Definition
Formally, the s-density bundle Vols(M) of a differentiable manifold M is obtained by an associated bundle construction, intertwining the one-dimensional group representation
of the general linear group with the frame bundle of M. More precisely,
The resulting line bundle is known as the bundle of s-densities, and is denoted by
A 1-density is also referred to simply as a density.
More generally, the associated bundle construction also allows densities to be constructed from any vector bundle E on M.
In detail, if (Uα,φα) is an atlas of coordinate charts on M, then there is associated a local trivialization of
subordinate to the open cover Uα such that the associated GL(1)-cocycle satisfies
Read more about this topic: Density On A Manifold
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