Renormalization of One-Dimensional Semirelativistic Bosons with Contact Interactions
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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BibTeX
@misc{erman2026renormalization,
title = {{Renormalization of One-Dimensional Semirelativistic Bosons with Contact Interactions}},
author = {Fatih Erman and O. Teoman Turgut},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09068},
eprint = {2609.09068},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09068},
}
RIS
TY - UNPB
TI - Renormalization of One-Dimensional Semirelativistic Bosons with Contact Interactions
AU - Fatih Erman
AU - O. Teoman Turgut
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.09068
UR - https://arxiv.org/abs/2609.09068
AB - 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.
ER -