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Journal of Physics Conference Series

Supersymmetric harmonic oscillator and nonlinear supercoherent states

Erik Díaz-Bautista, David J. Fernández C.

Published Apr 13, 2015• 2 citations
Publisher

Abstract

We find and analyze the (nonlinear) supercoherent states associated with the generalized nonlinear supersymmetric annihilation operator (SAO) of the supersymmetric harmonic oscillator. We discuss as well the uncertainty relation for a special case in order to compare our results with those obtained for the linear supercoherent states.
DOI
10.1088/1742-6596/597/1/012031

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This study generalizes the supersymmetric coherent states introduced by Aragone and Zypman in 1986. The Hamiltonian of the supersymmetric quantum harmonic oscillator leads to the definition of the generalized supersymmetric annihilation operators as a 3-parameter family. Their eigenstates are the generalized supercoherent states, which can be calculated explicitly for three relevant regions of parameter space. The uncertainty in position and momentum is discussed, with specific concentration on where the uncertainty is saturated, where it is bounded, and where it is unbounded.
A general approach is presented for constructing coherent states for supersymmetric systems. It uses Rogers's supermanifold formulation of supergroups to extend the group-theoretic method. Supercoherent states are explicitly obtained for the supersymmetric harmonic oscillator. They are shown to be eigenstates of the supersymmetric annihilation operator and to be minimum-uncertainty states. Two more-complex situations with extended physical supersymmetries are also considered: an electron moving in a constant magnetic field, and the electron-monopole system. The supercoherent states for these systems are found using super Baker-Campbell-Hausdorff relations and their interpretation is elucidated.