Renormalization of One-Dimensional Semirelativistic Bosons with Contact Interactions

• URL: http://arxiv.org/abs/2609.09068v1
• Date: Tue, 08 Sep 2026 17:22:36 GMT
• Title: Renormalization of One-Dimensional Semirelativistic Bosons with Contact Interactions
• Abstract summary: We study one-dimensional spinless bosons with semirelativistic spinless-Salpeter dispersion and attractive pairwise contact interactions.<n>We construct the renormalized many-body theory using an enlarged Fock space and a Schur-complement representation of the resolvent.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study one-dimensional spinless bosons with semirelativistic spinless-Salpeter dispersion and attractive pairwise contact interactions. Because the dispersion becomes linear at large momentum, the contact interaction is marginal by power counting and produces a logarithmic ultraviolet divergence. We construct the renormalized many-body theory using an enlarged Fock space and a Schur-complement representation of the resolvent, eliminating 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. We treat the two-body problem explicitly and show, in the norm-resolvent sense, that the nonrelativistic limit reproduces the attractive Lieb--Liniger Hamiltonian. We also formulate a mean-field approximation directly within the renormalized theory. In the massless and deeply bound large-particle-number regimes, it predicts an exponentially increasing binding scale whose exponent is determined by a one-dimensional variational problem.

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