Electrically-charged hadrons in a finite box

When aiming at a percent precision in hadronic quantities calculated by means of lattice simulations, isospin breaking effects become relevant. These are of two kinds: up/down mass splitting and electromagnetic corrections. In order to properly account for the latter, a consistent formulation of electrically-charged states in finite volume is needed. On a periodic torus, Gauss’ law and large gauge transformations forbid the propagation of electrically-charged states.

I will discuss a setup initially proposed by Wiese and Polley, and based on the use of so-called C* boundary conditions: fields are periodic around the torus up to charge conjugation. We will see that a certain class of electrically-charged states can be constructed in a fully consistent fashion, without relying on gauge fixing. This class is determined by the residual symmetries of the theory in finite volume, and covers most of the interesting phenomenological applications in the framework of numerical simulations. Some peculiar finite-volume effects will be discussed.