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The application of N=2 supersymmetric quantum mechanics for the quantizationof homogeneous systems coupled with gravity is discussed. Starting with thesuperfield formulation of an N=2 SUSY sigma model, Hermitian self-adjointexpressions for quantum Hamiltonians and Lagrangians for any signature of asigma-model metric are obtained. This approach is then applied to coupled SU(2)Einstein-Yang-Mills (EYM) systems in axially symmetric $Bianchi$-type I, II,VIII, IX, $Kantowski-Sachs$, and closed $Friedmann-Robertson-Walker$cosmological models. It is shown that all these models admit the embedding intothe N=2 SUSY sigma model with the explicit expressions for superpotentialsbeing direct sums of gravitational and Yang-Mills (YM) parts. In addition, theYM parts of superpotentials exactly coincide with the correspondingChern-Simons terms. The spontaneous SUSY breaking caused by YM instantons inEYM systems is discussed in a number of examples.Comment: 17 pages, REVTeX, no figures; minor corrections, few ref's added; to  appear in Phys. Rev. D58, Dec. 15, 1998 issu

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Towards<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mn /></mml:math>SUSY homogeneous quantum cosmology: Einstein-Yang-Mills systems

TowardsN=2SUSY homogeneous quantum cosmology: Einstein-Yang-Mills systems