General results for the Witten index using the Wigner-Kirkwood expansion

Bhaduri, R. K. ; Khare, Avinash ; Murthy, M. V. N. (1989) General results for the Witten index using the Wigner-Kirkwood expansion Modern Physics Letters A, 4 (27). pp. 2701-2704. ISSN 0217-7323

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Official URL: http://www.worldscinet.com/mpla/04/0427/S021773238...

Related URL: http://dx.doi.org/10.1142/S0217732389003002

Abstract

A systematic ħ-expansion of the regulated Witten index Δ(β) in one and two-dimensional SUSY quantum mechanics reveals that the lowest order ħ-term is nonzero, and all terms to at least the next four orders vanish. In one dimension, this lowest order term yields the well-known exact quantum result for an arbitrary superpotential. For the Pauli Hamiltonian with an arbitrary vector potential in two-dimensions, we find the new result that the semiclassical Δ(β) is β-independent and is equal to the number of magnetic flux lines.

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