A theoretical study has addressed the renormalization of one-dimensional spinless bosons, characterized by semirelativistic Salpeter dispersion and attractive pairwise contact interactions. The peculiarity of this dispersion is that it becomes linear at large momenta, implying that the contact interaction is marginal by power counting and generates a logarithmic ultraviolet divergence. This work is crucial for developing a consistent many-body theory in systems where short-range interactions are significant and the semirelativistic nature of the particles cannot be ignored.

The researchers constructed a renormalized many-body theory using an enlarged Fock space and a Schur-complement representation of the resolvent. This approach allowed for the elimination of the bare coupling in favor of the physical zero-total-momentum two-body bound-state energy. The resulting cutoff-independent resolvent defines a self-adjoint Hamiltonian in each fixed particle-number sector. The validity of this method was explicitly demonstrated for the two-body problem, showing that the nonrelativistic limit reproduces the attractive Lieb-Liniger Hamiltonian, a fundamental model in condensed matter physics.

Furthermore, the study formulated a mean-field approximation directly within the renormalized theory. In the massless and deeply bound large-particle-number regimes, this approximation predicts an exponentially increasing binding energy scale. The exponent of this growth is determined by a one-dimensional variational problem. These results open new avenues for understanding and modeling many-body quantum systems with semirelativistic interactions, with potential implications for condensed matter physics and ultracold systems.