Wavelets And Renormalization

This text describes the role played by wavelet decompositions in quantum field theory. The author postpones the particle interpretation and begins with abstract quantum physics. The quantization of the classical scalar field and of the classical electromagnetic field are then reviewed, and the most basic axiomatic fied theory is discussed. F unctional integrals for imaginary-time-ordered expectations are also introduced, and the connection with classical statistical mechanics and the development of cluster expansion are both emphasized heavily. The renormalization group formalism is developed from the point of view of wavelets, which are closey related to Gaussian fixed points. The ultraviolet renormalization problem is also reviwed. The text concludes with a discussion on the construction and properties of various types of wavelets.