Abstract
A nonperturbative computation is propozed for the renormalized Green’s function of a massless real-valued scalar field \(\phi\) on the background generated by a two-dimensional zero-range potential localized on an infinite straight line. Such a potential corresponds to the exotic limit \(\xi\to\infty\) , \(\beta^{\prime}\sim 1/\xi\) of the vacuum polarization problem near a cosmic string. The approach implies the renormalization of the delta-coupling constant \(\lambda\) . The renormalized Euclidean and Hadamard Green’s functions are presented in equivalent forms as single-variable integrals with integrands being transcendent functions. Using the renormalized Hadamard function, the renormalized vacuum expectation values of the field squared and of the energy–momentum tensor operator are computed. Asymptotic cases are analyzed in detail.
