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Diagonalizing Quadratic Bosonic Operators by Non-Autonomous Flow Equations

Volker Bach Technische Universität Braunschweig, Germany
Jean-Bernard Bru Universidad del País Vasco, Bilbao, Spain and Basque Center for Applied Mathematics, Bilbao, Spain and Basque Foundation for Science, Bilbao, Spain
Available Formats:
Electronic ISBN: 978-1-4704-2828-0
Product Code: MEMO/240/1138.E
List Price: $83.00 MAA Member Price:$74.70
AMS Member Price: $49.80 Click above image for expanded view Diagonalizing Quadratic Bosonic Operators by Non-Autonomous Flow Equations Volker Bach Technische Universität Braunschweig, Germany Jean-Bernard Bru Universidad del País Vasco, Bilbao, Spain and Basque Center for Applied Mathematics, Bilbao, Spain and Basque Foundation for Science, Bilbao, Spain Available Formats:  Electronic ISBN: 978-1-4704-2828-0 Product Code: MEMO/240/1138.E  List Price:$83.00 MAA Member Price: $74.70 AMS Member Price:$49.80
• Book Details

Memoirs of the American Mathematical Society
Volume: 2402015; 122 pp
MSC: Primary 47; 81;

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.

• Chapters
• 1. Introduction
• 2. Diagonalization of Quadratic Boson Hamiltonians
• 3. Brocket–Wegner Flow for Quadratic Boson Operators
• 4. Illustration of the Method
• 5. Technical Proofs on the One–Particle Hilbert Space
• 6. Technical Proofs on the Boson Fock Space
• 7. Appendix
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Volume: 2402015; 122 pp
MSC: Primary 47; 81;

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.

• Chapters
• 1. Introduction
• 2. Diagonalization of Quadratic Boson Hamiltonians
• 3. Brocket–Wegner Flow for Quadratic Boson Operators
• 4. Illustration of the Method
• 5. Technical Proofs on the One–Particle Hilbert Space
• 6. Technical Proofs on the Boson Fock Space
• 7. Appendix
Review Copy – for reviewers who would like to review an AMS book
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