Diffeomorphism Invariant Actions for Partial Systems

Abstract

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.

5 pages (10 preprint pages) ReVTeX

References in corpus (4)

• The Black Hole in Three Dimensional Space Time
• On Pair Creation of Extremal Black Holes and Kaluza-Klein Monopoles
• Gauge Invariance for Generally Covariant Systems
• Complex Numbers, Quantum Mechanics and the Beginning of Time

Cited by in corpus (4)

• Flat entanglement spectra in fixed-area states of quantum gravity
• Edge states in Gravity and Black Hole Physics
• Mass Superselection, Canonical Gauge Transformations, and Asymptotically Flat Variational Principles
• Boundary conditions from boundary terms, Noether charges and the trace K lagrangian in general relativity