Discretising quantum field theory using wavelets

In this thesis, I develop a new discretisation scheme offered by wavelet analysis. Daubechies wavelets of orderK ≥3 are used to encode the quantum field theory of the 1D transverse Ising model in a discrete approximation. I then analytically determine the energy spectrum, which is used to construct the correlation matrix. This allows for the calculation of bipartite von Neumann entropy,which acts a measure of entanglement entropy for block spin chains. These results are qualitativelyand quantitatively compared to the discrete and continuous Ising models as a gauge of the method'ssuccess as an alternative discretisation scheme.