  Discrete wavelet-based methods promise to emerge as an excellent framework
for the non-perturbative analysis of quantum field theories. In this work, we
investigate aspects of renormalization in theories analyzed using wavelet-based
methods. We demonstrate the non-perturbative approach of regularization,
renormalization, and the emergence of flowing coupling constant within the
context of these methods. This is tested on a model of the particle in an
attractive Dirac delta function potential in two spatial dimensions, which is
known to demonstrate quintessential features found in a typical relativistic
quantum field theory.
