  We prove an equivariant index theorem on the Euclidean space using a
continuous field of $C^*$-algebras. This generalizes the work of Elliott,
Natsume and Nest, which is a special case of the algebraic index theorem by
Nest-Tsygan. Using our formula, the equivariant index of the Bott-Dirac
operator on $\mathbb{R}^{2n}$ can be explicitly calculated.
