29,018 research outputs found
Generalised Hamiltonian embedding of the Proca model
We convert the second class Proca model into a first class theory by using
the generalised prescription of Batalin, Fradkin and Tyutin. We then show how a
basic set of gauge invariant fields in the embedded model can be identified
with the fundamental fields in the proca model as well as with the observables
in the St\"uckelberg model or in the model involving the interaction of an
abelian 2-form field with the Maxwell field. The connection of these models
with the massive Kalb-Ramond model is also elucidated within a path integral
approach.Comment: 11 pages, Latex, No figur
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-
An interacting scalar field and the recent cosmic acceleration
In this paper it is shown that the Brans - Dicke scalar field itself can
serve the purpose of providing an early deceleration and a late time
acceleration of the universe without any need of quintessence field if one
considers an interaction, i.e, transfer of energy between the dark matter and
the Brans - Dicke scalar field.Comment: 10 pages, 2 figure
A method of estimating the average derivative: the multivariate case
The paper uses local linear regression to estimate the ``direct'' Average Derivative \delta = E(D[m(x)]), where m(x) is the regression function. The estimate of \delta is the weighted average of local slope estimates. We prove the asymptotic normality of the estimate under conditions which are different from the conditions used by Heardle-Stoker (H-S) (1989). Using Monte-Carlo simulation experiments we give some small sample results comparing our estimator with the H-S estimator under our conditions for asymptotic normality.
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