Discreti̇zation of quantum fi̇eld theories using haar wavelet basis

This doctoral thesis consists of five chapters and the introduction section provides information about field expressions in physics in chronological order. In this section, the problem of degrees of freedom is mentioned while expressing quantum field theories. The wavelets to be used to bring the infinite number of degrees of freedom in quantum field theory to finite convergence through discretization are expressed in the second section. Accordingly, the mathematical structure and integrals of the Haar wavelet family are also expressed in this section. In the third section, classical and quantum field theories and the Lagrangian and Hamiltonian expressions in these fields are discussed in detail, and the general definitions of these expressions are made based on the studies in the literature. In the fourth section, the discretization operations of the equations of quantum field theories, which is the general purpose of the study, are performed. In this section, the suitability of the structure of the Haar wavelet bases for the approach to the Hamiltonian equation is expressed. In this section, the approach to the solution is discussed in two different ways. This section provides important data for us to see the advantages and disadvantages of the model.