nLab configuration space (physics)

Idea

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

For example the configuration space of $n \in \mathbb{N}$ point particles that roam around in some manifold $X$ (e.g. thought of as physical space) is the $n$-fold Cartesian product $X^n$. If the particles are constrained not to be at coincident points, then the configuration space is the corresponding subspace of $X^n$. 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 configurations of fields on (an open subset of) spacetime. This is then called the space of trajectories or space of histories of the system.

Examples

• in gravity: Wheeler superspace

Related concepts

• configuration space (mathematics)

• space of field histories

• phase space