On the super-conformal quantum mechanics in the nonlinear realizations approach

V.P Akulov,Oktay Cebecioglu,A Pashnev

doi:10.1016/s0370-2693(03)00547-1

Abstract

In the framework of nonlinear realizations we rederive the action of the N=2 super-conformal quantum mechanics (SCQM). We propose also the WZNW-like construction of interaction term in the Lagrangian with the help of Cartan's Omega-forms.

Highlights

The Conformal Quantum Mechanics (CQM)[1] as well as its supersymmetric generalization – SuperConformal Quantum Mechanics (SCQM) [2]-[3] are the simplest theories for developing the methods of investigation of more complicated higher dimensional field theories
The nonlinear realizations method leads to the lagrangians, which may be constructed in the framework of the usual superfield approach in which supersymmetry is realized linearly in the standard manner
One of the goals of the present paper is to show that the consistent application of the nonlinear realizations approach gives the possibility of constructing both the kinetic and interaction terms for CQM and N = 2 SCQM in the superfield approach without using the inverse Higgs effect

Summary

Introduction

The Conformal Quantum Mechanics (CQM)[1] as well as its supersymmetric generalization – SCQM [2]-[3] are the simplest theories for developing the methods of investigation of more complicated higher dimensional field theories. The nonlinear realizations method leads to the lagrangians, which may be constructed in the framework of the usual superfield approach in which supersymmetry is realized linearly in the standard manner In deriving of these results from the nonlinear realizations approach the Cartan’s Omegaforms technics is usually supplied by the so called inverse Higgs effect [13]. One of the goals of the present paper is to show that the consistent application of the nonlinear realizations approach gives the possibility of constructing both the kinetic and interaction terms for CQM and N = 2 SCQM in the superfield approach without using the inverse Higgs effect. The application of the method developed in the first part of the paper gives us the possibility to construct from the Cartan’s Omega-forms the interaction part of the superfield action as well

Conformal group and its matrix representation

The action integral for Conformal Mechanics

Conclusions