nLab
target space

Context

\infty-Chern-Simons theory

∞-Chern-Weil theory

∞-Chern-Simons theory

∞-Wess-Zumino-Witten theory

Ingredients

Definition

Examples

Quantum field theory

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

Contents

Idea

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

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.

Examples

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.

Revised on May 22, 2012 21:30:31 by Urs Schreiber (89.204.139.56)