Reducing the Chern–Simons term by a symmetry

Reducing a 3-dimensional Chern–Simons term by a symmetry yields other topologically interesting structures. Specifically, reducing by radial symmetry results in a 1-dimensional quantum mechanical model, which has recently been used in an analysis of finite-temperature Chern–Simons theory. The radially symmetric expression may be inserted into 3-dimensional monopole or (2+1)-dimensional instanton equations, where it eliminates the monopole or instanton solutions.