The Chern-Simons state for topological invariants

Alberto Escalante (1, 2)

1 LUTH (UMR_8102) - Laboratoire Univers et Théories
2 Instituto de Física "Luis Rivera Terrazas" (IFUAP)

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.

Domaines: Astrophysique [astro-ph]

Alberto Escalante. The Chern-Simons state for topological invariants. Physics Letters B, 2009, 676, pp.105-111. ⟨10.1016/j.physletb.2009.04.052⟩. ⟨hal-03743104⟩