DOI 10.1007/s100529901050
Generalized Hamiltonian
formalism
of (2+1)-dimensional non-linear
-model
in polynomial formulation
Toyoki Matsuyama
Department of Physics, Nara University of Education, Takabatake-cho, Nara 630-8528, Japan (e-mail: matsuyat@nara-edu.ac.jp)
Received: 29 September 1998 / Published online: 14 January 1999
Abstract
We investigate the canonical structure of the (2+1)-dimensional non-linear
model in a polynomial formulation.
A current density defined in the non-linear model is a vector field,
which satisfies a formal flatness (or pure gauge) condition.
It is the polynomial formulation in which the vector field is regarded
as a dynamic variable on which the flatness condition is imposed as a
constraint condition by introducing a Lagrange multiplier field.
The model so formulated has gauge symmetry under a transformation of
the Lagrange multiplier field.
We construct the generalized Hamiltonian formalism of the model explicitly
by using the Dirac method for constrained systems.
We derive three types of the pre-gauge-fixing Hamiltonian systems:
In the first system the current algebra is realized as the fundamental Dirac
Brackets.
The second one manifests the similar canonical structure as the Chern-Simons
or BF theories.
In the last one there appears an interesting interaction as the dynamic
variables are coupled to their conjugate momenta via the covariant derivative.
Copyright Springer-Verlag
