Generalized Kahler Geometry in View of Supersymmetric Quantum Mechanics

This paper contains a detailed study of generalized Kahler geometry from the viewpoint of quantum 0+1-dimensional supersymmetric σ-model. Peierls brackets rather than canonical quantization are used to quantize the superclassical system. Supercharges (or relevant differential operators) are expressed explicitly and covariantly. Index theorems in this context are also discussed briefly.