The application of wavelets in field theory

Abstract

In this thesis, it has been studied and repeated C. Best and A. Schafer’s work on the application of wavelet to the Gaussian model and the Landau-Ginzburg model. The fields of the Gaussian model are expanded in wavelet representation and with the fluctuation strengths of wavelet coefficients as variational parameter, the free energy of the model in Gaussian ensemble is minimized analytically. We then numerically recalculate the fluctuation strengths of wavelet coefficients and thus the correlation function. The result confirms that wavelets provide a reasonable description of the critical phenomena with only a small number of variational parameters, which is the same as the application of wavelet in other fields. In Landau-Ginzburg model, by analytic approximation, it is shown how the phase-transition is represented in wavelet space and how critical exponents can be computed from the wavelet expansion.