Nonrelativistic supersymmetry in noncommutative space (original) (raw)

(2 + 1)-Dimensional models with a Chern-Simons-like term and noncommutative geometry

Reports on Mathematical Physics, 1999

We consider new D = 2 nonrelativistic model of classical mechanics providing via the Noether theorem the (2+1)-Galilean symmetry algebra with two central charges: the mass m and the coupling constant k of a Chem-Simons-like term. We discuss the interpretation of k as describing the noncommutativity of D = 2 space coordinates. We quantize the model and show that it describes the superposition of a free motion in noncommutative D = 2 space as well as the "internal" oscillator modes. We add a suitably chosen class of velocity-dependent two-particle interactions, which is described by local potentials in D = 2 noncommutative space. We show that the indefinite metric due to the third-order time derivative term in the field equations, even in the presence of interactions, can be eliminated by the imposition of a subsidiary condition.

Noncommutative Chern-Simons soliton

Physical Review D, 2004

We have studied the noncommutative extension of the relativistic Chern-Simons-Higgs model, in the first non-trivial order in θ, with only spatial noncommutativity. Both Lagrangian and Hamiltonian formulations of the problem have been discussed, with the focus being on the canonical and symmetric forms of the energy-momentum tensor. In the Hamiltonian scheme, constraint analysis and the induced Dirac brackets have been provided. The spacetime translation generators and their actions on the fields are discussed in detail.

Symmetries of Non-relativistic Field Theories on the Non-Commutative Plane ∗

2005

New developments on non-relativistic field theoretical models on the non commutative plane are reviewed. It is shown in particular that Galilean invariance strongly restricts the admissible interactions. Moreover, if a scalar field is coupled to a Chern Simons gauge field, a geometrical phase emerges for vortex like solutions, transformed by Galilei boosts. Non commutative solitons finite action solutions of the classical equations of motion of noncommutative field theories have attracted great interest in the last few years, mainly in connection with strings and brane dynamics [1]. However, at very low energy (i.e. in condensed matter physics), the analysis of the Fractional Quantum Hall Effect (FQHE) [2], has suggested that the phenomenology can be expressed in terms of quasi-particles, related to states of strongly correlated electrons in the Lowest Landau Level. These quasi-particles are imbedded into an effective gauge connection of entirely quantum mechanical nature, related t...

Supersymmetric non-Abelian non-commutative Chern–Simons theory

Physics Letters B, 2006

In this work, we study the three-dimensional non-Abelian noncommutative supersymmetric Chern-Simons model with the U (N ) gauge group. Using a superfield formulation, we prove that, for the pure gauge theory, the Green functions are one-loop finite in any gauge, if the gauge superpotential belongs to the fundamental representation of u(N ); this result also holds when matter in the fundamental representation is included. However, the cancellation of both ultraviolet and ultraviolet/infrared infrared divergences only happens in a special gauge if the coupling of the matter is in the adjoint representation. We also look into the finite one-loop quantum corrections to the effective action: in the pure gauge sector the Maxwell together with its corresponding gauge fixing action are generated; in the matter sector, the Chern-Simons term is generated, inducing a shift in the classical Chern-Simons coefficient. * Electronic address: alysson,mgomes,ajsilva@fma.if.usp.br † Electronic address: petrov@fisica.ufpb.br

On duality of the noncommutative extension of the Maxwell–Chern–Simons model

Physics Letters B, 2005

We study issues of duality in 3D field theory models over a canonical noncommutative spacetime and obtain the noncommutative extension of the self-dual model induced by the Seiberg–Witten map. We apply the dual projection technique to uncover some properties of the noncommutative Maxwell–Chern–Simons theory up to first-order in the noncommutative parameter. A duality between this theory and a model similar to the ordinary self-dual model is established. The correspondence of the basic fields is obtained and the equivalence of algebras and equations of motion are directly verified. We also comment on previous results in this subject.

On duality of the noncommutative supersymmetric Maxwell-Chern-Simons theory

Physics Letters B, 2008

We study the possibility of establishing the dual equivalence between the noncommutative supersymmetric Maxwell-Chern-Simons theory and the noncommutative supersymmetric self-dual theory. It turns to be that whereas in the commutative case the Maxwell-Chern-Simons theory can be mapped into the sum of the self-dual theory and the Chern-Simons theory, in the noncommutative case such a mapping is possible only for the theory with modified Maxwell term.

a New Approach to the Analysis of a Noncommutative Chern-Simons Theory

Modern Physics Letters A, 2006

A novel approach to the analysis of a noncommutative Chern--Simons gauge theory with matter coupled in the adjoint representation has been discussed. The analysis is based on a recently proposed closed form Seiberg--Witten map which is exact in the noncommutative parameter.