Multidimensional quantization. V: The mechanical systems with supersymmetry (Q756217)

[For part I-IV see ibid. 5, No.2, 42-55 (1980; Zbl 0502.58019), ibid. 7, No.1, 87-93 (1982; Zbl 0571.58012), ibid. 8, No.1, 59-72 (1983; Zbl 0569.58021), and ibid. 13, No.1, 67-72 (1988; Zbl 0693.58007).] Using the new notion of polarization developed in Parts I and II of this contribution, the author proposes a supersymmetry approach to the quantization problem of the Hamiltonian systems with supersymmetry. The main result is the construction of the multidimensional quantization procedure using Hilbert superbundles with connection and some so-called weak Lagrangian invariant tangent superdistributions (called superpolarizations). In particular, we prove that the derivatives of the representations induced from the superpolarizations are just the Lie superalgebra representations deduced from the multidimensional quantization.