Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-12-21
Nucl.Phys. B662 (2003) 413-446
Physics
High Energy Physics
High Energy Physics - Theory
33 pages, REVTeX4, typos corrected
Scientific paper
10.1016/S0550-3213(03)00341-9
We derive the necessary and sufficient condition for Type A N-fold supersymmetry by direct calculation of the intertwining relation and show the complete equivalence between this analytic construction and the sl(2) construction based on quasi-solvability. An intimate relation between the pair of algebraic Hamiltonians is found. The classification problem on Type A N-fold supersymmetric models is investigated by considering the invariance of both the Hamiltonians and N-fold supercharge under the GL(2,K) transformation. We generalize the Bender-Dunne polynomials to all the Type A N-fold supersymmetric models without requiring the normalizability of the solvable sector. Although there is a case where weak orthogonality of them is not guaranteed, this fact does not cause any difficulty on the generalization. It is shown that the anti-commutator of the Type A N-fold supercharges is expressed as the critical polynomial of them in the original Hamiltonian, from which we establish the complete Type A N-fold superalgebra. A novel interpretation of the critical polynomials in view of polynomial invariants is given.
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