On (2+1)Dimensional Topologically Massive Non-linear Electrodynamics

The (2+1) dimensional non-linear electrodynamics, the so called Pagels–Tomboulis electrodynamics, with the Chern–Simons term is considered. We obtain ”generalized self–dual equation” and find the corresponding generalized massive Chern–Simons Lagrangian. Similar results for (2+1) massive dilaton electrodynamics have been obtained. 1 The Pagels–Tomboulis model Among many gauge theories the Pagels–Tomboulis model [1] L = − 4 ( F a μνF aμν Λ )δ−1 F a μνF aμν (1) has a special place. Here F a μν = ∂μA a ν − ∂νAaμ − ǫabcAbμAcν is the standard field tensor, δ is a dimensionless parameter and Λ is a dimensional constant. The gauge field is SU(2) type i.e. a = 1, 2, 3. One can check that this Lagrangian has positively defined energy for δ ≥ 1 2 . The model was originally found as an effective model for the low energy (3+1) QCD [1]. In fact, it was shown that electrical sources are confined for [email protected] [email protected]