Relativistic Three-Body Equations in a Wavelet Basis

We show how to use Daubechies' wavelets to reduce the relativistic Faddeev-Lovelace equations to approximate linear equations with sparse matrices. We transform the equations to a form where the spectator and two-body relative momenta are separated. We use the renormalization group equation for the scaling basis functions [1][2] to accurately and efficiently compute scaling basis matrix elements of the transformed three-body kernel with moving singularities. The wavelet transform provides a fast (O(N)) mapping from the scaling basis to the wavelet basis, where the kernel can be accurately approximated by a sparse matrix. \newline [1] B. Kessler, G. L. Payne, W. N. Polyzou, Phys. Rev. C70,034003(2004). \newline [2] B. M. Kessler, G. L. Payne, W. N. Polyzou Few-Body Systems, 33,1(2003).