  We present the {\em (symmetry-incorporating) formalism of general continuum
models with boundary conditions} and apply it to the model with the minimal
number of degrees of freedom necessary to have a well-defined boundary: a model
with a two-component wave function and a linear-in-momentum Hamiltonian. We
derive the most general forms (class A) of both the Hamiltonian and boundary
condition in 1D (insulator), 2D (quantum anomalous Hall insulator), and 3D
(Weyl node) and analytically calculate and explore the corresponding general
bound/edge/surface-state structures. In 1D, one bound state exists in the half
of the $\text{U}(1)$ parameter space of possible boundary conditions.
Considering several dimensions simultaneously ties the models together and
uncovers important relations between them. We formulate a version of
bulk-boundary correspondence that fully characterizes the vicinity of a Weyl
point: the chirality of the surface-state spectrum along a path enclosing the
projected Weyl point is equal to the Chern number of the Weyl point. We
demonstrate how symmetries are naturally incorporated into the formalism, by
deriving the most general form of the model with chiral symmetry (class AIII).
We show that the (perhaps unexpected) existence of persistent bound states in
the topologically trivial 1D class-A model is not accidental and has at least
two topological explanations, by relating it to the topologically nontrivial 2D
class-A (by viewing it as an effective 2D quantum anomalous Hall system) and 1D
class-AIII (via deviation from the cases of chiral symmetry in the parameter
space) models. We identify this as a systematic "propagation effect", whereby
bound states from topologically nontrivial classes, where they are protected
and guaranteed to exist, propagate to the related, "adjacent" in dimension or
symmetry, topologically trivial classes.
