N=4 Supersymmetric Multidimensional Quantum Mechanics, Partial SUSY Breaking and Superconformal Quantum Mechanics

摘要

The multidimensional N=4 supersymmetric quantum mechanics (SUSY QM) is constructed using the superfield approach. As a result the component form of the classical and quantum Lagrangian and Hamiltonian is obtained. In the considered SUSY QM both classical and quantum N=4 algebras include central charges and it opens various possibilities for the partial supersymmetry breaking. It is shown, that the quantum mechanical models with one quarter, one half and three quarters of the 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 the one half or total supersymmetry breakdown. We illustrate the constructed general formalism, as well as all possible cases of the partial SUSY breaking on the example, which is the direct multidimensional generalization of the one-dimensional N=4 superconformal quantum mechanical model. Some open questions and possible applications of the constructed multidimensional N=4 SUSY QM to the known exactly integrable systems and to the problems of quantum cosmology are briefly discussed.