briefly added some of the standard argument to the proof of the heat-kernel expression for the index of the Dirac operator here
(prompted by this PhysicsOverflow question).
]]>expanded at index the section For Dirac operators with a tad more details on the statement
I gave index an Idea-section.
In the course of this I created some stubby auxiliary entries, such as (in rapidly increasing order of stubbieness)
]]>