Quantisation of second class systems in the Batalin-Tyutin formalism

Journal Article · Tue Aug 01 04:00:00 EDT 1995 · Annals of Physics (New York)

DOI:https://doi.org/10.1006/aphy.1995.1062· OSTI ID:110900

Banerjee, N ^[1]; Banerjee, R ^[2]; Ghosh, S ^[3]

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1. Saha Institute of Nuclear Physics, Calcutta (India)
2. S.N. Bose National Centre for Basic Sciences, Calcutta (India)
3. Gobardanga Hindu College, West Bengal (India)

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 Batalin-Tyutin analysis may be generalised, particularly if one is dealing with nonabelian theories. In order to gain a deeper insight into 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 Stueckelberg scalar. Some comments are also made concerning the corresponding identification in the nonabelian example. 23 refs.

• OSTI ID: 110900
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 2 Vol. 241; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
HAMILTONIANS
LAGRANGIAN FUNCTION
PHASE SPACE
QUANTIZATION