Chern–Simons form

In mathematics, the Chern–Simons forms are certain secondary characteristic classes.

[1] The theory is named for Shiing-Shen Chern and James Harris Simons, co-authors of a 1974 paper entitled "Characteristic Forms and Geometric Invariants," from which the theory arose.

The right-hand side of this equation is proportional to the k-th Chern character of the connection

In general, the Chern–Simons p-form is defined for any odd p.[4] In 1978, Albert Schwarz formulated Chern–Simons theory, early topological quantum field theory, using Chern-Simons forms.

[5] In the gauge theory, the integral of Chern-Simons form is a global geometric invariant, and is typically gauge invariant modulo addition of an integer.