Euclidean functional integral approach for disorder variables and kinks

Abstract

We propose and investigate an euclidean functional integral approach for the construction of local kink operators and disorder variables. The main difference from the existing quasiclassical approach is the emphasis on local fields instead of kink states and collective coordinate methods. We show that all two-dimensional kink fields emerge from the gauge theory of matter fields in Bohm-Aharonov fluxes. In the case of real scalar or self-conjugate Majorana fields the language of “flat non-trivial fibre bundles” is unavoidable since there is no minimal coupling to a vector potential. As an application we reproduce the construction of the Ising field theory and related models. In this way we obtain a unified treatment of the work of Sato et al. with that of other authors.