Higher Chern-Simons based on (2-)crossed modules

Abstract

Abstract We present higher Chern-Simons theories based on (2-)crossed modules. We start from the generalized differential forms in Generalized Differential Calculus and define the corresponding generalized connections which consist of higher connections. Then we establish the generalized Chern-Simons forms to get the higher Chern-Simons actions. Finally, we develop the higher second Chern forms and Chern-Weil theorems.

Keywords

• Higher Gauge Theories
• Chern-Simons Theories
• Gauge Symmetry
• Topological Field Theories