  In this paper we define (local) Dirac operators and magnetic Schr\"odinger
Hamiltonians on fractals and prove their (essential) self-adjointness. To do so
we use the concept of 1-forms and derivations associated with Dirichlet forms
as introduced by Cipriani and Sauvageot, and further studied by the authors
jointly with R\"ockner, Ionescu and Rogers. For simplicity our definitions and
results are formulated for the Sierpinski gasket with its standard self-similar
energy form. We point out how they may be generalized to other spaces, such as
the classical Sierpinski carpet.
