nLab target space



\infty-Chern-Simons theory

∞-Chern-Weil theory

∞-Chern-Simons theory

∞-Wess-Zumino-Witten theory




Quantum field theory


physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes

theory (physics), model (physics)

experiment, measurement, computable physics



Generally, for Maps(Σ,X)Maps(\Sigma,X) a mapping space, the space or spacetime XX is the corresponding target space or target spacetime.

Specifically, in a sigma-model quantum field theory a field configuration over a parameter space Σ\Sigma is a morphism ΣX\Sigma \to X to some object XX. This is the target space of the theory. The σ\sigma-model is to be understood as describing the quantum mechanics of branes with trajectories of shape Σ\Sigma propagating in XX.


For sigma-models that are supposed to describe quantum objects in the observed world (such as the relativistic particle) the target space XX would be our spacetime. But the target space can be something more general or more exotic. For instance in Dijkgraaf-Witten theory the target space is the classifying space of a discrete group.

Last revised on January 18, 2015 at 22:25:40. See the history of this page for a list of all contributions to it.