**Memoirs of the American Mathematical Society**

2015;
122 pp;
Softcover

MSC: Primary 47; 81;

Print ISBN: 978-1-4704-1705-5

Product Code: MEMO/240/1138

List Price: $83.00

Individual Member Price: $49.80

**Electronic ISBN: 978-1-4704-2828-0
Product Code: MEMO/240/1138.E**

List Price: $83.00

Individual Member Price: $49.80

# Diagonalizing Quadratic Bosonic Operators by Non-Autonomous Flow Equations

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*Volker Bach; Jean-Bernard Bru*

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.

#### Table of Contents

# Table of Contents

## Diagonalizing Quadratic Bosonic Operators by Non-Autonomous Flow Equations

- Cover Cover11
- Title page i2
- Chapter I. Introduction 18
- Chapter II. Diagonalization of Quadratic Boson Hamiltonians 310
- Chapter III. Brocket–Wegner Flow for Quadratic Boson Operators 1118
- Chapter IV. Illustration of the Method 1926
- Chapter V. Technical Proofs on the One–Particle Hilbert Space 2734
- Chapter VI. Technical Proofs on the Boson Fock Space 7582
- Chapter VII. Appendix 101108
- References 121128
- Back Cover Back Cover1134