Canonical quantization of theories containing fractional powers of the d'Alembertian operator

Abstract

The authors present a canonical formulation for theories whose actions contain noninteger powers of the d'Alembertian operator and which were recently shown to play a central role in (2+1)-dimensional bosonization. They show that these theories possess an infinite number of constraints and use the Dirac method in order to obtain the classical brackets. The causal and classical Green functions are obtained and their meaning in terms of field expectation values is discussed. The Wightman functions are introduced and shown to lead to the microcausality principle. A mode expansion for the field is obtained. This permits the re-obtainment of the Wightman functions as vacuum expectation values of products of the basic fields. Creation and annihilation operators are naturally introduced but, as shown, they are not related to definite mass particle states. This is also confirmed by the spectral decomposition of the Wightman functions.