N=4 supersymmetric multidimensional quantum mechanics, partial SUSY breaking, and superconformal quantum mechanics - art. no. 043512

The multidimensional N=4 supersymmetric (SUSY) quantum mechanics (QM) is co nstructed using the superfield approach. As a result, the component form of the classical and quantum Lagrangian and Hamiltonian is obtained. In the S USY QM considered, both classical and quantum N=4 algebras include central charges, and this opens various possibilities for partial supersymmetry bre aking. It is shown that quantum-mechanical models with one-quarter, one-hal f, and three-quarters of unbroken (broken) supersymmetries can exist in the framework of the multidimensional N=4 SUSY QM, while the one-dimensional N =4 SUSY QM, constructed earlier, admits only one half or total supersymmetr y breakdown. We illustrate the constructed general formalism, as well as al l possible cases of partial SUSY breaking taking as an example a direct mul tidimensional generalization of the one-dimensional N=4 superconformal quan tum-mechanical model. Some open questions and possible applications of the constructed multidimensional N=4 SUSY QM to the known exactly integrable sy stems and problems of quantum cosmology are briefly discussed.