  I introduce a modification of continuous matrix product states (CMPS) that
makes them adapted to relativistic quantum field theories (QFT). These
relativistic CMPS can be used to solve genuine 1+1 dimensional QFT without UV
cutoff and directly in the thermodynamic limit. I explain the intuition for the
modification, and show all the computations needed for the optimization of the
ansatz. I illustrate the method on the self-interacting scalar field, a.k.a.
the $\phi^4_2$ model. The numerical results obtained are truly variational, and
thus provide rigorous energy upper bounds.
