  In this paper, we give a quantum interpretation of the Bismut-Chern character
form (the loop space lifting of the Chern character form) as well as the Chern
character form associated to a complex vector bundle with connection over a
smooth manifold in the framework of supersymmetric quantum field theories
developed by Stolz and Teichner \cite{ST07}. We show that the Bismut-Chern
character form comes up via a loop-deloop process when one goes from $1|1$D
theory over a manifold down to a $0|1$D theory over its free loop space. Based
on our quantum interpretation of the Bismut-Chern character form and Chern
character form, we construct Chern character type maps for SUSY QFTs.
