دانلود کتاب Pseudo-Bosons and Their Coherent States (Mathematical Physics Studies)

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Preface
Acknowledgments
Contents
1 Introduction
References
2 Bosons and Pseudo-Bosons
2.1 Few Essential Mathematical Ingredients
2.1.1 A Taste of Unbounded Operators
2.1.2 Biorthogonal Systems
2.2 Bosonic Operators
2.3 Deforming the CCR: General Results
2.4 Regular Pseudo-Bosons
2.5 Shifted Ladder Operators
2.6 D-PBs from Superpotentials
2.6.1 Back to the Regular Case
2.6.2 Recovering the Shifted Ladder Operators
2.7 Ladders from the Swanson Model
2.8 Relations Between Bosons and Pseudo-Bosons
References
3 Other Ladder Operators
3.1 Pseudo-Fermions
3.1.1 Deforming the CAR
3.2 Pseudo-Quons
3.2.1 D-Pseudo Quons
3.3 Deformed Generalized Heisenberg Algebra
3.3.1 Deformed GHA
3.3.2 Constructing a DGHA from a GHA
3.4 Abstract Ladder Operators
3.4.1 ALOs for H0=H0
The Case [Z,Z]=1 1
3.5 ALO for H≠H
3.6 Conclusions
References
4 Our Way to the BCH Formula
4.1 The Operators eγc and eγc
4.2 Products of eαc and eβc
4.3 Commuting eαc and eβc
4.3.1 Some Auxiliary Results
4.3.2 Back to (4.16)
4.4 The BCH Formula
4.5 More Results
4.6 BCH and Related Formulas Outside Le
References
5 Bi-Coherent States
5.1 A First General Approach
5.1.1 Reproducing Kernels
5.2 Introducing the Deformed Displacement Operators
5.3 Bi-Coherent States for the Shifted Ladder Operators
5.4 Regular Pseudo-Bosons
5.4.1 Useful Results
5.4.2 Back to Regular Pseudo-Bosons
5.5 Swanson Model and Other Unbounded Deformations
5.5.1 More Useful Results
5.5.2 Back to Bi-Coherent States
References
6 Examples of Bi-coherent States
6.1 Bi-coherent States for Regular Pseudo-Bosons, I
6.1.1 Specializing η(x)
6.2 Bi-coherent States for Regular Pseudo-Bosons, II
6.3 Bi-coherent States for Shifted Ladder Operators
6.4 Bi-coherent States for the Swanson Hamiltonian
6.5 A Last Comment on the Examples and on BCSs
References
7 Weak Pseudo-Bosons and Related Bi-coherent States
7.1 A First Appearance of Weak Pseudo-Bosons
7.1.1 Weak Pseudo Bosons and the Damped HarmonicOscillator
7.2 Some Preliminary Results on Weak Bi-coherent States
7.3 What Else?
References
8 An Application to Transition Probability
8.1 Preliminary Aspects on Quantum Dynamics for H≠H
8.1.1 Transition Probabilities and Consequences
8.1.2 Extending These Results
8.2 Bi-Coherent States and the Propagator
8.2.1 Direct Computation
8.2.2 Indirect, But Still Exact, Computation
8.2.3 Indirect Perturbative Computation
8.3 Final Comments
References
9 Conclusions
References
A More Formulas and Results
A.1 Appendix: Derivation of (2.35) and of W(α,β)
A.2 Appendix: Estimates of \"026B30D n\"026B30D 2
A.3 Appendix: Some Simple Checks for the Adjoint in Le
A.4 Appendix: Some Other Checks for the Adjoint in R
A.5 Appendix: on W(α,β) and S(α,β)
A.6 Appendix: A Sum Rule
A.7 Appendix: A Decay Property for Functions in S(R)
A.8 Appendix: Some Integrals from Coherent States
Index