Massless sine-Gordon and massive Thirring models: Proof of Coleman's equivalence (Q2517976)

One of the most fascinating aspects of QFT is the phenomenon of bosonization; fermionic systems can be mapped in bosonic ones and vice versa. The simplest example is provided by the equivalence between free massless Dirac fermions and free massless bosons. Such equivalence can be extended to interacting theories; Coleman showed the equivalence, in the zero charge sector, between massive Thirring model and the massless sine-Gordon model. In this paper the authors present a proof of Coleman's equivalence between the Euclidean massive Thirring model with a small interaction and the mass term restricted to a fixed finite volume and the Euclidean massless sine-Gordon model with interaction restricted to the same volume. They follow the Coleman strategy, but an extension of multiscale techniques yield the convergence of the expansion.