Non-analyticity of the S-matrix with spontaneously broken Lorentz invariance

A bstract We study the S -matrix of Goldstones in the renormalizable theory of a U(1) complex scalar at finite charge, i.e. in a state that breaks Lorentz invariance. The theory is weakly coupled so that this S -matrix exists at all energies. Unlike the Lorentz invariant case, the resulting S -matrix is not analytic in the exchanged (complexified) four-momentum. The non-analyticities stem from the LSZ reduction formula, as a consequence of the energy-dependent mixing between the radial and Goldstone modes.