nLab configuration space (physics)

Redirected from "space of field configurations".
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Context

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

Contents

Idea

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 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

Last revised on May 7, 2024 at 17:44:28. See the history of this page for a list of all contributions to it.