Yang-Mills theories in the light-cone gauge

We develop the Hamiltonian quantization of Yang-Mills theories in the light-cone gauge, obtaining the well-defined prescription for the gluon propagator, previously proposed in the literature. A Hilbert space with indefinite metric emerges in which the role of the residual gauge freedom is clarified. It is possible to define consistently a subspace with positive-semidefinite inner product where Gauss’s law and Poincaré covariance are recovered and the perturbative S matrix is unitary.