Renormalization of bosonic quadratic Hamiltonians involving rank-one perturbations

2025/06/10 by Gamet, Thomas
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2506.08590

Abstract

In this article, we study the renormalization of a bosonic quadratic Hamiltonian with an ultraviolet divergence. The Hamiltonian is composed of the sum of a free energy and the square of the smeared field operator. We explicitly diagonalize the Hamiltonian via Bogoliubov transformations, and the diagonalized Hamiltonian is easier to study. We show a renormalization of both the energy and the coupling constant depending on the form factor of the interaction.

Citations

• Ultraviolet Renormalization of Spin Boson Models I. Normal and 2-Nilpotent Interactions
• Ultraviolet Renormalisation of a Quantum Field Toy Model II
• Self-adjointness and domain of generalized spin-boson models with mild ultraviolet divergences
• Implementing Bogoliubov Transformations Beyond the Shale-Stinespring Condition
• The Random Phase Approximation for Interacting Fermi Gases in the Mean-Field Regime
• The Massless Nelson Hamiltonian and its Domain
• Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations
• Bogoliubov spectrum of interacting Bose gases
• Bogoliubov Hamiltonians and one parameter groups of Bogoliubov transformations

Related

• Ultraviolet Renormalization of the Nelson Hamiltonian through Functional Integration
• Ultraviolet Renormalisation of a Quantum Field Toy Model II
• Ultraviolet Renormalisation of a quantum field toy model I
• Recent advances in the theory of Bogoliubov Hamiltonians
• Linearized renormalization