Supersymmetric embedding of a model of a quantum harmonic oscillator interacting with infinitely many bosons

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Abstract
A mathematically rigorous analysis is given on supersymmetric embedding of a model of a one-dimensional quantum harmonic oscillator interacting with infinitely many bosons moving in the s-dimensional space Rs. The model is exactly soluble. By a rigorous explicit construction of supersymmetric quantum field theories, it was proven that the Hamiltonian of the model is supersymmetrically embeddable if it is non-negative. The index of the Dirac–Kähler-type operators associated with the supercharges of the supersymmetric quantum field theories is computed.