= Twisted Dirac operator
{c}
{title2=$D_W=c\circ\nabla^{S\otimes W}$}
On a <spin manifold>, tensor the <spinor bundle> $S$ with a <Hermitian vector bundle> $W$ carrying a <unitary connection>. Composing the induced tensor-product <connection on a vector bundle> with <Clifford multiplication> defines the twisted Dirac operator. In even dimension it maps $S^+\otimes W$ to $S^-\otimes W$ and conversely. On a <closed manifold> its chiral restriction $D_W^+:H^1(S^+\otimes W)\to L^2(S^-\otimes W)$ is a <Fredholm operator>.
Back to article page
