TL;DR
This paper develops a unified gauge theory framework in 2+1 dimensions to study various models like Maxwell-Chern-Simons and Proca, using advanced quantization methods and demonstrating their equivalences.
Contribution
It constructs a comprehensive master gauge theory in both Lagrangian and Hamiltonian formalisms, unifying multiple models and reproducing known equivalences through BRST and symplectic quantization.
Findings
Unified master gauge theory in 2+1 dimensions.
Reproduction of the Deser-Jackiw equivalence from the extended model.
Application of BRST and symplectic quantization to gauge theories.
Abstract
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.
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