Two supersymmetric classical mechanical systems are discussed. Concrete realizations are obtained by supposing that the dynamical variables take values in the Grassmann algebra with two generators. The equations of motion are explicitly solved, and the action of the supergroup on the space of solutions is elucidated. The Lie algebra of the supergroup is the even part of the tensor product where 𝒢 is the super Lie algebra of supersymmetries and time translations. For each system, the solutions with zero energy need to be constructed separately. For these Bogomolny-type solutions, the orbit of the supergroup is smaller than in the generic case.
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B. De Witt, Supermanifolds, 2nd ed. (Cambridge University Press, Cambridge, 1992).
2.
P. G. O. Freund, Introduction to Supersymmetry (Cambridge University Press, Cambridge, 1986).
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© 1999 American Institute of Physics.
1999
American Institute of Physics
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