The Chern–Simons state for topological invariants

Abstract

The covariant canonical formalism for the second Chern and Euler topological invariants which depends of a connection valued in the Lie algebra of SO(3,1) is performed. We show that the Chern–Simons state corresponds to an eigenfunction of zero energy for such characteristic classes, in particular, for the Euler class within self-dual (or anti-self-dual) scenario. In addition, to complete our analysis we develop the Hamiltonian analysis for the theories under study, obtaining a best description of the results obtained with the symplectic method.