| eBook 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 |
| eBook 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 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 240; 2015; 122 ppMSC: 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.
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Table of Contents
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Chapters
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1. Introduction
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2. Diagonalization of Quadratic Boson Hamiltonians
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3. Brocket–Wegner Flow for Quadratic Boson Operators
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4. Illustration of the Method
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5. Technical Proofs on the One–Particle Hilbert Space
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6. Technical Proofs on the Boson Fock Space
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7. Appendix
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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
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7. Appendix
