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arXiv · 2506.08590

Renormalization of bosonic quadratic Hamiltonians involving rank-one perturbations

Thomas Gamet
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Abstract

We study the renormalization of a bosonic quadratic Hamiltonian with an ultraviolet divergence. The Hamiltonian is composed of the sum of a free part and the square of the smeared field operator. We explicitly diagonalize the Hamiltonian via Bogoliubov transformations, thus simplifying its definition as a self-adjoint operator. Depending on the field operator's smearing, we discuss different renormalizations, either of the energy alone, or the energy and coupling constant together.

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Thomas Gamet. 2025-06-10. Renormalization of bosonic quadratic Hamiltonians involving rank-one perturbations. https://arxiv.org/abs/2506.08590

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