Bosonic quadratic Hamiltonians

Abstract

We discuss self-adjoint operators given formally by expressions quadratic in bosonic creation and annihilation operators. We give conditions when they can be defined as self-adjoint operators, possibly after an infinite renormalization. We also discuss explicit formulas for their infimum. Our main motivation comes from Local Quantum Field Theory, which furnishes interesting examples of bosonic quadratic Hamiltonians that require an infinite renormalization.

In the 1st version Theorem 3.11 was incorrect. Main changes in the 2nd version is correction of this mistake and a more detailed introduction

References in corpus (1)

• The BCS functional of superconductivity and its mathematical properties

Cited by in corpus (24)

• Spin cat states in a ferromagnetic insulator
• Symmetry and topological classification of Floquet non-Hermitian systems
• Optimal rate of condensation for trapped bosons in the Gross-Pitaevskii regime
• Squaring the fermion: The threefold way and the fate of zero modes
• Restoring number conservation in quadratic bosonic Hamiltonians with dualities
• Entanglement entropy and Fisher information metric for closed bosonic strings in homogeneous plane wave background
• Scaling limits of bosonic ground states, from many-body to nonlinear Schr{ö}dinger
• Quantum geometry of bosonic Bogoliubov quasiparticles
• Bounds on the bipartite entanglement entropy for oscillator systems with or without disorder
• Bosons in a double well: two-mode approximation and fluctuations
• Open loop linear control of quadratic Hamiltonians with applications
• Topological bosonic Bogoliubov excitations with sublattice symmetry
• Classicality of the Bogoliubov transformations and the dynamical Casimir effect through the reduced state of the field
• A Quantum Information Perspective on Many-Body Dispersive Forces
• Bogoliubov Transformations Beyond Shale-Stinespring: Generic $v^{\ast }v$ for bosons
• Accelerated Gaussian quantum state transfer between two remote mechanical resonators
• The decoherence-free subalgebra of Gaussian Quantum Markov Semigroups
• Efficient trainability of linear optical modules in quantum optical neural networks
• Explicit Diagonalization of Pair Interaction Models
• On the Hartree-Fock-Bogoliubov equations
• Symplectic decomposition from submatrix determinants
• Spectral analysis of an abstract pair interaction model
• Quantization of Polaritons Confined in Dielectric Structures
• Reduced fluctuations for bosons in a double well