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We rederive the expansion of the Bergman kernel on Kahler manifolds developed by Tian, Yau, Zelditch, Lu and Catlin, using path integral and perturbation theory, and generalize it to supersymmetric quantum mechanics.
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X. Dai, K. Liu and X. Ma, “On the asymptotic expansion of Bergman kernel,” C. R. Acad. Sci. Paris, Ser. I
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M. R. Douglas, R. L. Karp, S. Lukic and R. Reinbacher, J. Math. Phys. 49
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