  An approach for solving scattering problems, based on two quantum field
theory methods, the heat kernel method and the scattering spectral method, is
constructed. This approach converts a method of calculating heat kernels into a
method of solving scattering problems. This allows us to establish a method of
scattering problems from a method of heat kernels. As an application, we
construct an approach for solving scattering problems based on the covariant
perturbation theory of heat-kernel expansions. In order to apply the
heat-kernel method to scattering problems, we first calculate the off-diagonal
heat-kernel expansion in the frame of the covariant perturbation theory.
Moreover, as an alternative application of the relation between heat kernels
and partial-wave phase shifts presented in this paper, we give an example of
how to calculate a global heat kernel from a known scattering phase shift.
