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M. Sivakumar

Publications and source records attributed to M. Sivakumar.

27 records · Page 2Linked to original sources
arXiv1999

Topologically Massive Abelian Gauge Theory From BFT Hamiltonian Embedding of A First-order Theory

We start with a new first order gauge non-invariant formulation of massive spin-one theory and map it to a reducible gauge theory viz; abelian $B{\wedge}F$ theory by the Hamiltonian embedding procedure of Batalin, Fradkin and Tyutin(BFT). This equivalence is shown from the equations of motion of the embedded Hamiltonian. We also demonstrate that the original gauge non-invariant model and the topologically massive gauge theory can both be obtained by suitable choice of gauges, from the phase space partition function of the emebedded Hamiltonian, proving their equivalence. Comparison of the first order formulation with the other known massive spin-one theories is also discussed.

hep-th↗
arXiv1998

Chiral Solitons in a Current Coupled Schrödinger Equation With Self Interaction

Recently non-topological chiral soliton solutions were obtained in a derivatively coupled non-linear Schrödinger model in 1+1 dimensions. We extend the analysis to include a more general self-coupling potential (which includes the previous cases) and find chiral soliton solutions. Interestingly even the magnitude of the velocity is found to be fixed. Energy and U(1) charge associated with this non-topological chiral solitons are also obtained.

cond-mat↗
arXiv1997

Generalized Haldane-Shastry Models as Supersymmetric Partners of the Calogero-Sutherland Type Models

We consider the supersymmetric Calogero-Sutherland type N-particle problems in one dimension and show that the corresponding fermionic part can be identified with the generalized X-Y models in the presence of an inhomogeneous magnetic field. In particular we show that the generalized Haldane-Shastry models (with magnetic field) are themselves the fermionic partners of the Calogero-Sutherland type models. Several such models are discussed and a recipe is given for constructing spin models and finding their ground state energy from the corresponding N-particle problems.

cond-mat.stat-mech↗
arXiv1996

Duality and Massive Gauge Invariant Theories

Two different massive gauge invariant spin-one theories in $3+1$ dimensions, one Stuckelberg formulation and the other `$B^{\wedge}F$' theory, with Kalb-Ramond field are shown to be related by duality. This is demonstrated by gauging the global symmetry in the model and constraining the corresponding dual field strength to be zero by a Lagrange multiplier, which becomes a field in the dual theory. Implication of this equivalence to the $5$ dimensional theories from which these theories can be obtained is discussed. The self-dual Deser-Jackiw model in $2+1$ dimensions, is also shown to result by applying this procedure to Maxwell-Chern-Simon theory.

hep-th↗
arXiv1995

On the $W$-algebra in the Calegero-Sutherland model using the Exchange operators

We study the $W_\infty$ algebra in the Calegero-Sutherland model using the exchange operators. The presence of all the sub-algebras of $W_\infty$ is shown in this model. A simplified proof for this algebra, in the symmetric ordered basics, is given. It is pointed out that the algebra contains in general, nonlinear terms. Possible connection to the nonlinear $W_\infty$ is discussed.

hep-th↗
arXiv1995

Laughlin Wave Function and One-Dimensional Free Fermions

Making use of the well-known phase space reduction in the lowest Landau level(LLL), we show that the Laughlin wave function for the $ν= {1\over m}$ case can be obtained exactly as a coherent state representation of an one dimensional $(1D)$ wave function. The $1D$ system consists of $m$ copies of free fermions associated with each of the $N$ electrons, confined in a common harmonic well potential. Interestingly, the condition for this exact correspondence is found to incorporate Jain's parton picture. We argue that, this correspondence between the free fermions and quantum Hall effect is due to the mapping of the $1D$ system under consideration, to the Gaussian unitary ensemble in the random matrix theory.

cond-mat↗
arXiv1993

O(3) Non-linear $σ$ model with Hopf term and Higher spin theories

Following our earlier work we argue in detail for the equivalence of the nonlinear $σ$ model with Hopf term at~$θ=π/2s$ ~and an interacting spin-s theory. We give an ansatz for spin-s operators in the $σ$ model and show the equivalence of the correlation functions.We also show the relation between topological and Noether currents. We obtain the Lorentz and discrete transformation properties of the spin-s operator from the fields of the $σ$ model. We also explore the connection of this model with Quantum Hall Fluids.

hep-th↗
arXiv1992

Is the $O(3)~σ$ Model with the Hopf Term Exactly Equivalent to a Higher Spin Theory?

We write down a local $CP_1$ model involving two gauge fields, which is exactly equivalent to the O(3) $σ$ model with the Hopf term. We impose the $CP_1$ constraint by using the gaussian representation of the delta function. For the coefficient of the Hopf term, $θ= {π\over 2s}$, 2s being an integer, we show that the resulting model is exactly equivalent to an interacting theory of spin-$s$ fields. Thus we conjecture that there should be a fixed point in the spin-$s$ theory near which it is exactly equal to the $σ$ model.

hep-th↗