Isospin symmetry is explicitly broken in the Standard Model by the non-zero differences of mass and electric charge between the up and down quarks. Both of these corrections are expected to have a comparable size of the order of one percent relativel
y to hadronic energies. Although these contributions are small, they play a crucial role in hadronic and nuclear physics. In this review we explain how to properly define QCD and QED on a finite and discrete space-time so that isospin corrections to hadronic observables can be computed ab-initio. We then consider the different approaches to compute lattice correlation functions of QCD and QED observables. Finally we summarise the actual lattice results concerning the isospin corrections to the light hadron spectrum.
At the precision reached in current lattice QCD calculations, electromagnetic effects are becoming numerically relevant. Here, electromagnetic effects are included by superimposing $mathrm{U}(1)$ degrees of freedom on $N_f = 2+1$ QCD configurations f
rom the Budapest-Marseille-Wuppertal Collaboration. We present preliminary results for the electromagnetic corrections to light pseudoscalars mesons masses and discuss some of the associated systematic errors.
