Rabin Banerjee

Batalin-Tyutin quantization of the CPN-1 model.

The

Duality symmetry and plane waves in non-commutative electrodynamics

CP^{N-1}

Noncommuting electric fields and algebraic consistency in noncommutative gauge theories

model is quantised in the generalised canonical formalism of Batalin and Tyutin by converting the original second class system into first class. Operator ordering ambiguities present in the conventional quantisation scheme of Dirac are thereby avoided. The first class constraints, the involutive Hamiltonian and the BRST charge are explicitly computed. The partition function is defined and evaluated in the unitary gauge.

Membrane and non-commutativity

Abstract We generalise the electric–magnetic duality in standard Maxwell theory to its non-commutative version. Both spacespace and spacetime non-commutativity are necessary. The duality symmetry is then extended to a general class of non-commutative gauge theories that goes beyond non-commutative electrodynamics. As an application of this symmetry, plane wave solutions are analysed. Dispersion relations following from these solutions show that, in the presence of spacetime non-commutativity, non-commutative electrodynamics admits two waves with distinct polarisations propagating at different velocities in the same direction.

Batalin-Tyutin Quantisation of the

We show that noncommuting electric fields occur naturally in

CP^{N-1}

theta

model

-expanded noncommutative gauge theories. Using this noncommutativity, which is field dependent, and a hamiltonian generalisation of the Seiberg-Witten Map, the algebraic consistency in the lagrangian and hamiltonian formulations of these theories, is established. A comparison of results in different descriptions shows that this generalised map acts as canonical transformation in the physical subspace only. Finally, we apply the hamiltonian formulation to derive the gauge symmetries of the action.

Symmetries of the general topologically massive gravity in the hamiltonian and lagrangian formalisms

Abstract We analyse the dynamics of an open membrane, both for the free case and when it is coupled to a background three-form, whose boundary is attached to p -branes. The role of boundary conditions and constraints in the Nambu–Goto and Polyakov formulations is studied. The low-energy approximation that effectively reduces the membrane to an open string is examined in detail. Non-commutative features of the boundary string coordinates, where the cylindrical membrane is attached to the D p -branes, are revealed by algebraic consistency arguments and not by treating boundary conditions as primary constraints, as is usually done. The exact form of the non-commutative algebra is obtained in the low-energy limit.

Black Hole Entropy from Covariant Anomalies

The

Noncommutativity in open string: a gauge independent analysis

CP^{N-1}