Heat kernels and zeta-function regularization for the mass of the supersymmetric kink

We apply zeta-function regularization to the kink and supersymmetric (SUSY) kink and compute its quantum mass. We fix ambiguities in the renormalization by considering the asymptotic expansion of the vacuum energy as the mass gap tends to infinity (while keeping scattering data fixed) and dropping all terms proportional to non-negative powers or the logarithm of this mass gap. As an alternative we write the regulated sum over zero point energies in terms of the heat kernel and apply standard heat kernel subtractions with modifications which take the boundaries into account. Finally we discuss to what extent these procedures are equivalent to the usual renormalization condition that tadpoles vanish.