Hewawasam, Kuravi2012-12-042012-12-042012-08https://hdl.handle.net/11299/140030University of Minnesota M.S. thesis. August 2012. Major: Physics. Advisor: John R Hiller. 1 computer file (PDF); viii, 82 pages, appendices A-B.This study is an application of wavelet numerical techniques in solving a non-perturbative Yukawa Hamiltonian in light-front quantum field theory. Once the problem is stated in the form of an integral equation, a wavelet basis of a particular scale is used to discretize the problem into a dense matrix. Wavelets are a class of functions with special properties. Daubachies wavelets are a subset of wavelets defined to have vanishing lower order moments, enabling Daubachies 2 and 3 wavelet bases to exactly represent polynomials of degree up to two. These properties make them useful as a basis set for various numerical methods. It was observed that a kernel containing structure in fine scales requires a fine scaling function basis to converge closer to analytical results. Once the kernel matrix is obtained, the wavelet transform followed by an absolute thresholding filters the dense kernel matrix to a sparse matrix. The sparse matrix eigenvalue problem was then solved and compared with the original eigenvalue problem. It was observed that as long as the problem is discretized with a scale fine enough to resolve the features of the kernel, higher levels of filtering would still reproduce eigenvalues that agree with the unfiltered problem.en-USFew-body problemsNumerical methodsQuantum field theoryWaveletsYukawa hamiltonianThesis or Dissertation