Diffeomorphism Invariant Actions for Partial Systems

Details Diffeomorphism Invariant Actions for Partial Systems Diffeomorphism Invariant Actions for Partial Systems

1994-11-28

arxiv.org/abs/gr-qc/9411067v1

Phys.Lett. B349 (1995) 89-93

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

5 pages (10 preprint pages) ReVTeX

Scientific paper

10.1016/0370-2693(95)00195-Q

Local action principles on a manifold $\M$ are invariant (if at all) only under diffeomorphisms that preserve the boundary of $\M$. Suppose, however, that we wish to study only part of a system described by such a principle; namely, the part that lies in a bounded region $R$ of spacetime where $R$ is specified in some diffeomorphism invariant manner. In this case, a description of the physics within $R$ should be invariant under {\it all} diffeomorphisms regardless of whether they preserve the boundary of this region. The following letter shows that physics in such a region can be described by an action principle that $i$) is invariant under both diffeomorphisms which preserve the boundary of $R$ and those that do not, $ii$) leaves the dynamics of the part of the system {\it outside} the region $R$ completely undetermined, and $iii$) can be constructed without first solving the original equations of motion.

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