Diagonalizing quadratic bosonic operators by non-autonomous flow equations / Volker Bach and Jean-Bernard Bru.

Includes bibliographical references.

Chapter 1. Introduction
Chapter 2. Diagonalization of Quadratic Boson Hamiltonians Chapter 3. Brocket-Wegner Flow for Quadratic Boson Operators Chapter 4. Illustration of the Method
Chapter 5. Technical Proofs on the One-Particle Hilbert Space Chapter 6. Technical Proofs on the Boson Fock Space Chapter 7. Appendix.

The authors study a non-autonomous, non-linear evolution equation on the space of operators on a complex Hilbert space. They specify assumptions that ensure the global existence of its solutions and allow them to derive its asymptotics at temporal infinity. They demonstrate that these assumptions are optimal in a suitable sense and more general than those used before. The evolution equation derives from the Brocket-Wegner flow that was proposed to diagonalize matrices and operators by a strongly continuous unitary flow. In fact, the solution of the non-linear flow equation leads to a diagonalization of Hamiltonian operators in boson quantum field theory which are quadratic in the field.