nLab configuration space (physics)




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The configuration space of a physical system is the space of all possible configurations of the system.

For example the configuration space of nn \in \mathbb{N} point particles that roam around in some manifold XX (e.g. thought of as physical space) is the nn-fold Cartesian product X nX^n. If the particles are constrained not to be at coincident points, then the configuration space is the corresponding subspace of X nX^n. This happens to be the kind of configuration space as typically considered in mathematics see at Fadell's configuration space.

In field theory over Lorentzian spacetime one is typically interested not in the configurations of fields “at a given time” (say on a fixed Cauchy surface) but in configuratios of fields on (an open subset of) spacetime. This is then called the space of trajectories or space of histories of the system.


Last revised on January 11, 2021 at 05:09:10. See the history of this page for a list of all contributions to it.