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Quantisation of second class systems in the Batalin-Tyutin formalism
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.Comment: 26 pages, Latex file, e-mail [email protected] SINP-TNP/94-
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.Comment: Accepted for publication in Annals of Physics (N.Y.
Dynamics of decoherence without dissipation in a squeezed thermal bath
We study a generic open quantum system where the coupling between the system
and its environment is of an energy-preserving quantum nondemolition (QND)
type. We obtain the general master equation for the evolution of such a system
under the influence of a squeezed thermal bath of harmonic oscillators. From
the master equation it can be seen explicitly that the process involves
decoherence or dephasing without any dissipation of energy. We work out the
decoherence-causing term in the high and zero temperature limits and check that
they match with known results for the case of a thermal bath. The decay of the
coherence is quantified as well by the dynamics of the linear entropy of the
system under various environmental conditions. We make a comparison of the
quantum statistical properties between QND and dissipative types of evolution
using a system of two-level atom and a harmonic oscillator.Comment: Accepted for publication in J. Phys. A: Math. Theor.; 23 pages, 8
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