Abstract
Discrete wavelet-based techniques hold the potential to establish a robust framework for the non-perturbative examination of quantum field theories. This study explores facets of renormalization within theories investigated through the wavelet-based framework. We showcase the non-perturbative application of regularization, renormalization, and the emergence of a flowing coupling constant within this framework. This is assessed using a model of a particle in an attractive 2-dimensional Dirac delta function potential in two spatial dimensions. This model is recognized for demonstrating fundamental features encountered in typical relativistic quantum field theories.
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