Multiresolution analysis of quantum theories using Daubechies wavelet basis

Flow equation methods, more generally known as Similarity Renormalization Group (SRG) techniques, were developed to address multiscale problems where multiple length or energy scales contribute simultaneously. In this Thesis, we formulate the flow equation method within a wavelet-based framework and apply it to study scale (resolution) separation in a two-dimensional scalar field theory. We demonstrate that the flow systematically block-diagonalizes the Hamiltonian with respect to wavelet resolution, achieving improved truncation compared to earlier studies. Using a model of two real scalar fields coupled through a quadratic interaction, we show that the flow equations effectively suppress couplings between low- and high-resolution degrees of freedom. This provides a clear mechanism for isolating low-resolution physics and offers insight into the construction of effective Hamiltonians using a wavelet-based flow equation approac