Abstract
In 1971 Patodi([2,3]) proved the local index theorem for two kinds of the classical geometric operators in the Atiyah-Singer theory. This article will improve the method used by Patodi and present a new proof of the local index theorem for the Dirac operator. The proof is so elementary that the Weyl invariant theorem, the topology and even the second Bianchi identity are not needed. At last of this article we point out that our method can work for other cl~ical operators.
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