Wavelets as basis functions in canonical quantization

Abstract

Canonical quantization of electromagnetic field is traditionally done using plane waves. It is possible to formulate the quantization using other complete set of basis functions. Wavelets are a special kind of functions which are localized in real as well as in Fourier space. In this paper we show how wavelets can be used as basis functions in canonical quantization. A countable set of mode functions are obtained. The general formalism of the change of basis is the same for all wavelets which satisfy a multiresolution analysis.