Unified Study of Planar Field Theories

A “Master” gauge theory is constructed in 2+1-dimensions through which various gauge invariant and gauge non-invariant theories can be studied. In particular, Maxwell-Chern-Simons, Maxwell-Proca and Maxwell-Chern-Simons -Proca models are considered here. The Master theory in an enlarged phase space is constructed both in Lagrangian (Stuckelberg) and Hamiltonian (Batalin-Tyutin) frameworks, the latter being the more general one, which includes the former as a special case. Subsequently, BRST quantization of the latter is performed. Lastly, the master Lagrangian, constructed by Deser and Jackiw (Phys. Lett. B139, (1984) 371), to show the equivalence between the Maxwell-Chern-Simons and the self-dual model, is also reproduced from our Batalin-Tyutin extended model. Symplectic quantization procedure for constraint systems is adopted in the last demonstration.