Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-03-09
Annals Phys. 241 (1995) 237-257
Physics
High Energy Physics
High Energy Physics - Theory
26 pages, Latex file, e-mail shila@saha.ernet.in SINP-TNP/94-2
Scientific paper
We review the Batalin-Tyutin approach of quantising second class systems which consists in enlarging the phase space to convert such systems into first class. The quantisation of first class systems, it may be mentioned, is already well founded. We show how the usual analysis of Batalin-Tyutin may be generalised, particularly if one is dealing with nonabelian theories. In order to gain a deeper insight into the formalism we have considered two specific examples of second class theories-- the massive Maxwell theory (Proca model) and its nonabelian extension. The first class constraints and the involutive Hamiltonian are explicitly constructed. The connection of our Hamiltonian approach with the usual Lagrangian formalism is elucidated. For the Proca model we reveal the importance of a boundary term which plays a significant role in establishing an exact identification of the extra fields in the Batalin-Tyutin approach with the St\"uckelberg scalar. Some comments are also made concerning the corresponding identification in the nonabelian example.
Banerjee Narayan
Banerjee Robi
Ghosh Sabyasachi
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