Classical Supersymmetric Mechanics

Details Classical Supersymmetric Mechanics Classical Supersymmetric Mechanics

2000-01-24

arxiv.org/abs/hep-th/0001155v1

Annals Phys. 284 (2000) 52-88

Physics

High Energy Physics

High Energy Physics - Theory

29 pages, 2 figures, submitted to Annals of Physics

Scientific paper

10.1006/aphy.2000.6057

We analyse a supersymmetric mechanical model derived from (1+1)-dimensional field theory with Yukawa interaction, assuming that all physical variables take their values in a Grassmann algebra B. Utilizing the symmetries of the model we demonstrate how for a certain class of potentials the equations of motion can be solved completely for any B. In a second approach we suppose that the Grassmann algebra is finitely generated, decompose the dynamical variables into real components and devise a layer-by-layer strategy to solve the equations of motion for arbitrary potential. We examine the possible types of motion for both bosonic and fermionic quantities and show how symmetries relate the former to the latter in a geometrical way. In particular, we investigate oscillatory motion, applying results of Floquet theory, in order to elucidate the role that energy variations of the lower order quantities play in determining the quantities of higher order in B.

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