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Electroweak gauginos with highly boosted hadronically decaying bosons at the LHC / / Yuta Okazaki
| Electroweak gauginos with highly boosted hadronically decaying bosons at the LHC / / Yuta Okazaki |
| Autore | Okazaki Yuta |
| Pubbl/distr/stampa | Singapore : , : Springer, , [2023] |
| Descrizione fisica | 1 online resource (230 pages) |
| Disciplina | 297.05 |
| Collana | Springer Theses |
| Soggetto topico | Bosons |
| ISBN |
9789811965937
9789811965920 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Supervisor's Foreword -- Preface -- Parts of this book have been published in the following journal articles -- Acknowledgements -- Contents -- Acronyms -- 1 Introduction -- References -- 2 Theoretical Background -- 2.1 The Standard Model -- 2.2 Supersymmetry -- 2.2.1 R-parity -- 2.2.2 SUSY Breaking -- 2.3 Minimal Supersymmetric Standard Model -- 2.3.1 Particle Contents in MSSM -- 2.3.2 Soft Breaking and the Soft Term in the MSSM Lagrangian -- 2.3.3 Gaugino Mass -- 2.3.4 SUSY Solutions of the SM Problems in the MSSM -- 2.3.5 Target Scenarios and Signal Models -- 2.3.6 Signal Topology -- 2.3.7 Current Limits by Collider Experiments -- 2.3.8 Current Limits by Other Experiments -- 2.4 Other SUSY Models -- 2.4.1 Soft Breaking Mechanism -- 2.4.2 General Gauge Mediation Scenario -- 2.4.3 Naturalness Driven Axino LSP Scenario -- References -- 3 Experimental Apparatus -- 3.1 Large Hadron Collider -- 3.2 ATLAS Detector -- 3.2.1 Coordinate Systems in ATLAS -- 3.2.2 Magnet System -- 3.2.3 Inner Detector -- 3.2.4 Calorimeters -- 3.2.5 Muon Spectrometer -- 3.2.6 Trigger and Data Acquisition -- References -- 4 Data and Monte Carlo Simulations -- 4.1 Recorded Data by the ATLAS Detector -- 4.2 Monte Carlo Simulation -- 4.2.1 Hard-Scatter Event Generation -- 4.2.2 SM Background Simulation -- 4.2.3 Signal Simulation Samples -- References -- 5 Physics Object Reconstruction -- 5.1 Overview -- 5.2 Tracks, Vertices, and Topo-clusters -- 5.3 Jets -- 5.3.1 Large-R Jet -- 5.3.2 Small-R Jet -- 5.3.3 Track Jet -- 5.4 Electrons and Photons -- 5.5 Muons -- 5.6 Object Selection -- 5.7 Missing Transverse Energy -- References -- 6 BosonTagging -- 6.1 Boosted W/Z Tagging -- 6.1.1 Overview -- 6.1.2 Optimization -- 6.1.3 Efficiency for Signal Jets -- 6.1.4 Efficiency for Background Jets -- 6.1.5 Physics Process Dependency -- 6.2 Vrightarrow bb Tagging Techinique.
References -- 7 Event Selection -- 7.1 Selection Strategy -- 7.2 Trigger Selection and Event Cleaning -- 7.3 Discriminating Variables -- 7.4 Preselection -- 7.5 Signal Region Selection -- 7.5.1 SR-4Q -- 7.5.2 SR-2B2Q -- References -- 8 Background Estimation -- 8.1 Strategy -- 8.2 Reducible Backgrounds Estimation -- 8.2.1 Overview -- 8.2.2 Control Regions -- 8.3 Validation for the Reducible Background Estimation -- 8.3.1 Preselection in 1L/1Y Categories -- 8.3.2 Definition of CRs and VRs in the 1L/1Y Categories -- 8.3.3 Comparison Between 0L/1L/1Y for V+jets MC -- 8.3.4 Jet Variable Comparison in the CRs and SRs/VRs -- 8.3.5 Transfer Factor Comparison -- 8.4 Physics Process Dependency in the Reducible Background Estimation and the Impact of the Composition Uncertainty -- 8.5 Irreducible Backgrounds Estimation -- Appendix -- References -- 9 Systematic Uncertainties -- 9.1 Large-R Jets -- 9.2 Boson Tagging Efficiency Uncertainty -- 9.3 Other Experimental Uncertainties -- 9.4 Theoretical Uncertainty -- 9.5 Summary of Systematic Uncertainties -- References -- 10 Results -- 10.1 Background Determination -- 10.2 Results on the Signal Regions -- 10.3 Model-Specific Exclusion Limits -- 10.3.1 (tildeW,tildeB)-SIM -- 10.3.2 (tildeW,tildeB), (tildeH,tildeB), (tildeW,tildeH) and (tildeH,tildeW) Models -- 10.3.3 (tildeH,tildeG) Model -- 10.3.4 (tildeH,tildea) Model -- References -- 11 Discussions -- 11.1 Future Prospects -- 11.1.1 Future Prospects of the Multi-lepton and Multi-b-and-1-Lepton analyses -- 11.1.2 Future Prospects of the Full-Hadronic Analysis -- 11.2 Implication to Dark Matter -- 11.2.1 tildeB-Like Dark Matter -- 11.2.2 tildeW-/tildeH-Like Dark Matter -- 11.3 Implication to Muon g-2 Anomaly -- 11.3.1 Light Electroweakino Scenarios Motivated by Muon g-2 Anomaly -- 11.4 Implication to Naturalness -- References -- 12 Conclusions. Appendix A Supersymmetry Framework -- A.1 Operator -- A.2 Gaugino Mass Eigenstates -- A.3 Grand Unified Theory -- A.4 Couplings between Z/h and the Lightest Neutralino -- A.5 Muon g-2 Contribution of SUSY Particles -- A.6 Gauge Mediated Symmetry Breaking -- Appendix B Event Cleaning -- B.1 Event Cleaning Based on Detector Responses -- B.2 Dead Tile Module Jets Veto -- B.3 Non-collision Background Veto -- B.4 Track Jets Cleaning -- Appendix C Event Display. |
| Record Nr. | UNINA-9910637714103321 |
Okazaki Yuta
|
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| Singapore : , : Springer, , [2023] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Interacting boson model from energy density functionals / / Kosuke Nomura
| Interacting boson model from energy density functionals / / Kosuke Nomura |
| Autore | Nomura Kosuke |
| Edizione | [1st ed. 2013.] |
| Pubbl/distr/stampa | Tokyo, : Springer Japan, 2013 |
| Descrizione fisica | 1 online resource (193 p.) |
| Disciplina | 539.74 |
| Collana | Springer Theses, Recognizing Outstanding Ph.D. Research |
| Soggetto topico |
Bosons
Physics Magnetism |
| ISBN |
1-299-33766-X
4-431-54234-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Basic Notions -- Rotating Deformed Systems with Axial Symmetry -- Weakly Deformed Systems with Triaxial Dynamics -- Comparison with Geometrical Model -- Is axially Asymmetric Nucleus Gamma Rigid or Unstable? -- Ground-state Correlation -- Summary and Concluding Remarks. |
| Record Nr. | UNINA-9910437978603321 |
|
Nomura Kosuke
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| Tokyo, : Springer Japan, 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The physics of the dark photon : a primer / / Marco Fabbrichesi, Emidio Gabrielli, Gaia Lanfranchi
| The physics of the dark photon : a primer / / Marco Fabbrichesi, Emidio Gabrielli, Gaia Lanfranchi |
| Autore | Fabbrichesi Marco |
| Edizione | [1st ed. 2021.] |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (X, 78 p. 19 illus., 17 illus. in color.) |
| Disciplina | 539.721 |
| Collana | SpringerBriefs in Physics |
| Soggetto topico |
Photons
Dark matter (Astronomy) Bosons |
| ISBN | 3-030-62519-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Introduction -- Phenomenology of the Massless Dark Photon -- Phenomenology of the Massive Dark Photon -- Concluding Remarks. |
| Record Nr. | UNISA-996466730303316 |
|
Fabbrichesi Marco
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||
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
The physics of the dark photon : a primer / / Marco Fabbrichesi, Emidio Gabrielli, Gaia Lanfranchi
| The physics of the dark photon : a primer / / Marco Fabbrichesi, Emidio Gabrielli, Gaia Lanfranchi |
| Autore | Fabbrichesi Marco |
| Edizione | [1st ed. 2021.] |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (X, 78 p. 19 illus., 17 illus. in color.) |
| Disciplina | 539.721 |
| Collana | SpringerBriefs in Physics |
| Soggetto topico |
Photons
Dark matter (Astronomy) Bosons |
| ISBN | 3-030-62519-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Introduction -- Phenomenology of the Massless Dark Photon -- Phenomenology of the Massive Dark Photon -- Concluding Remarks. |
| Record Nr. | UNINA-9910739474703321 |
|
Fabbrichesi Marco
|
||
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Pseudo-Bosons and their coherent states / / Fabio Bagarello
| Pseudo-Bosons and their coherent states / / Fabio Bagarello |
| Autore | Bagarello Fabio <1964-> |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (208 pages) |
| Disciplina | 539.721 |
| Collana | Mathematical Physics Studies |
| Soggetto topico |
Commutation relations (Quantum mechanics)
Bosons |
| ISBN |
9783030949990
9783030949983 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910564691003321 |
|
Bagarello Fabio <1964->
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||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Pseudo-Bosons and their coherent states / / Fabio Bagarello
| Pseudo-Bosons and their coherent states / / Fabio Bagarello |
| Autore | Bagarello Fabio <1964-> |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (208 pages) |
| Disciplina | 539.721 |
| Collana | Mathematical Physics Studies |
| Soggetto topico |
Commutation relations (Quantum mechanics)
Bosons |
| ISBN |
9783030949990
9783030949983 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISA-996472060003316 |
|
Bagarello Fabio <1964->
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
The theory of the Jahn-Teller effect : when a boson meets a fermion / / Arnout Ceulemans
| The theory of the Jahn-Teller effect : when a boson meets a fermion / / Arnout Ceulemans |
| Autore | Ceulemans Arnout |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (429 pages) |
| Disciplina | 530.143 |
| Soggetto topico |
Interacting boson-fermion models
Jahn-Teller effect Efecte Jahn-Teller Bosons Fermions |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783031095283
9783031095276 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- Part I Bosons and Fermions -- 1 The Impossible Theorem -- Contents -- 1.1 The Jahn-Teller Theorem -- 1.2 Charge Density Analysis -- 1.2.1 Occupation of dz2 -- 1.2.2 Occupation of dx2-y2 -- 1.2.3 Sum and Difference Orbitals -- 1.2.4 Orthogonal and Unitary Combinations -- 1.3 Outlook -- References -- 2 Bosons and Fermions -- Contents -- 2.1 Bosons -- 2.1.1 The Schrödinger Formalism -- 2.1.2 The Dirac Formalism -- 2.1.3 The Bargmann Mapping -- 2.2 Fermions -- 2.2.1 Fermion Operators -- 2.2.2 One-Electron Interactions -- 2.2.3 Quasi-Spin -- References -- 3 Boson-Fermion Interactions -- Contents -- 3.1 The Jahn-Teller Effect in a Triangular Molecule: A Toy Model -- 3.1.1 The Hückel Hamiltonian -- 3.1.2 Fermions: Trigonal Molecular Orbitals -- 3.1.3 Bosons: Vibrational Modes -- 3.1.4 Coupling Coefficients -- 3.2 Degeneracies and Time Reversal -- 3.2.1 Time Reversal -- 3.2.2 Irreducible Representations of the First Kind and Orthogonal Lie Groups -- 3.2.3 Irreducible Representations of the Second Kind and Symplectic Lie Groups -- 3.2.4 Irreducible Representations of the Third Kind -- 3.3 The Jahn-Teller Hamiltonian -- 3.4 Selection Rules -- 3.4.1 Space Symmetry -- 3.4.2 Time Reversal Symmetry -- 3.4.3 Hole-Particle Exchange Symmetry -- 3.5 Proof of the Jahn-Teller Theorem -- 3.5.1 History -- 3.5.2 Where Do Degeneracies Come From? -- 3.5.2.1 Cosets and the Positional Representation -- 3.5.2.2 Doubly Transitive Orbits -- 3.5.3 Degenerate Representations and Jahn-Teller Modes -- 3.5.4 Jahn-Teller Activity in Simplexes -- References -- Part II Dynamic Symmetries -- 4 The Rabi Hamiltonian -- Contents -- 4.1 The Adiabatic Potential -- 4.2 The Quantum Model -- 4.3 Bargmann Mapping of the Wave Equations -- 4.4 Eigenvalues -- 4.4.1 Classification of the Roots -- 4.4.2 Recurrence Relations and Transcendental Function.
4.4.3 The Rabi Spectrum -- 4.5 The Quantization of the Rabi Hamiltonian -- 4.6 Analyticity -- 4.7 Inversion Tunneling in Ammonia -- References -- 5 The E ×e Orbital Doublet -- Contents -- 5.1 The Quantum Model -- 5.2 Dynamic Symmetries -- 5.2.1 Boson Symmetry -- 5.2.2 Fermion Symmetry -- 5.2.3 Coupled Symmetries -- 5.3 The Canonical Form of the Wave Equation -- 5.4 Recurrence Relationships -- 5.5 Results -- 5.6 Discussion -- 5.7 Application: Na3 and the (E+A)×e Hamiltonian -- References -- 6 The Spin Quartet Γ8 ×(e+t2) System and the Symplectic Group Sp(4) -- Contents -- 6.1 Historical Note: Judd and Reik -- 6.2 The Hamiltonian -- 6.2.1 The Static Case -- 6.2.2 The Dynamic Hamiltonian -- 6.3 Sp(4) Fermion Symmetry -- 6.4 SO(5) Boson Symmetry -- 6.5 The Γ8 ×(e+t2) Dynamic Equations -- 6.6 The Γ8 ×t2 Subsystem -- 6.6.1 SO(3) Invariance -- 6.6.2 Dynamic Equations -- 6.7 Application -- 6.7.1 ReF6 -- 6.7.2 IrF6 -- References -- 7 Ansatz for the Jahn-Teller Triplet Instability -- Contents -- 7.1 SO(5) Symmetry and the Five-Dimensional Harmonic Oscillator -- 7.1.1 SU(5) ↓ SO(5) Symmetry Breaking -- 7.1.2 SO(5) ↓ SO(3) Symmetry Breaking -- 7.2 The Hamiltonian -- 7.3 The Vibrating Sphere -- 7.4 Boson Functions -- 7.4.1 S States -- 7.4.2 D States -- 7.4.3 F States -- 7.5 The Ansatz -- 7.6 The Jahn-Teller Equations -- 7.7 Solution -- 7.8 Ansatz for Vibronic D States -- 7.9 Application -- 7.10 Conclusion -- References -- 8 The Icosahedral Quartet and SO(9) ↓ SO(4) Symmetry Breaking -- Contents -- 8.1 Introduction -- 8.2 Preamble: Hyperspherical Symmetry -- 8.3 The Hamiltonian -- 8.4 The Vibrations of the Four-Dimensional Hypersphere -- 8.5 SO(9) ↓ SO(4) Symmetry Breaking -- 8.5.1 (0,0) Modes -- 8.5.2 (1,1) Boson Modes -- 8.5.3 Modes with Seniority ν> -- 4 -- 8.6 The Ansatz: Vibronic (12,12) Levels -- 8.7 Icosahedral Symmetry Lowering. 8.8 Application: C20 and C80 Fullerenes -- 8.8.1 C20 -- 8.8.2 C80 -- References -- 9 SO(14) ↓ SO(5) Symmetry Breaking and the Jahn-Teller Quintet Instability -- Contents -- 9.1 Dynamic Symmetries -- 9.2 Descent to Spherical Symmetry -- 9.2.1 Branching Rules for SO(5) SO(3) -- 9.2.2 The L=2 Case -- 9.2.3 The L=4 Case -- 9.3 Descent to Permutational Symmetry -- 9.3.1 The Icosahedral Hamiltonian -- 9.3.2 The Hexateron -- 9.4 Correlation Between the Spherical and the Permutational Scheme -- 9.5 Application: The Ground State of C60+ Cation -- References -- 10 Jahn's and Teller's Last Case: The Spinor Sextet -- Contents -- 10.1 Group Theory of the Sextet Spinor -- 10.1.1 The Unitary Symplectic Group USp(6) -- 10.1.2 The SO(14) Group of the Bosons -- 10.2 The Γ9 ×(g+2h) Problem -- 10.2.1 The Hamiltonian -- 10.2.2 Diagonalization -- 10.2.3 The Equal Coupling Case -- 10.3 Chemical Applications -- 10.4 Overview -- 10.4.1 Orbital Representations: SO(N) ⊃ SO(n) -- 10.4.2 Spinor Representations: SO(N) ⊃ USp(2n) -- References -- Part III Topography -- 11 Conical Intersections and Quantum Fields -- Contents -- 11.1 The Berry Phase -- 11.1.1 The Quantal Phase Factor Accompanying Adiabatic Changes -- 11.1.1.1 Single-Valued Basis Functions -- 11.1.1.2 Real Basis Sets -- 11.1.2 Holonomy -- 11.2 The E×e Jahn-Teller Case -- 11.2.1 Berry Phase for the E×e Case -- 11.2.2 The Dirac Monopole Analogy -- 11.2.3 Berry Phase and Angular Momentum -- 11.3 Quadruple Spin Degeneracy and the Instanton -- 11.3.1 The Γ8 ×t2g Hamiltonian -- 11.3.2 The Γ8 ×(eg+t2g) Hamiltonian -- References -- 12 Topography and Chemical Reactivity -- Contents -- 12.1 Tools -- 12.1.1 The Epikernel Principle -- 12.1.2 The Isostationary Function -- 12.1.3 Proof of the Epikernel Principle -- 12.1.3.1 Only One Λ Irrep -- 12.1.3.2 More than One Λ Irrep -- 12.1.3.3 Illustration: The Γ×(Λ1+Λ2) Problem. 12.2 Orbital Doublets -- 12.2.1 The E×(b1+b2) System -- 12.2.2 The E×e System -- 12.2.3 The Pentagonal E1×e2 Problem -- 12.3 The Cubic T×(e+t2) Problem -- 12.3.1 Second-Order Warping Terms -- 12.3.2 Chemical Reactivity: The Isomerization of Fe(CO)4 -- 12.4 The Icosahedral T ×h System -- 12.5 The Icosahedral G×g+h Quartet System -- 12.5.1 The Isostationary Function -- 12.5.2 Tetrahedral Minima -- 12.5.3 Trigonal Minima -- 12.6 The Icosahedral H×(g+2h) Quintet System -- 12.6.1 The Isostationary Function -- 12.6.2 Pentagonal Minima -- 12.6.3 Trigonal Minima -- 12.7 The Icosahedral Γ9 ×(g+2h) Sextet System -- 12.7.1 The G-Type Subspace -- 12.7.2 The H Subspace -- 12.7.2.1 The FH2 Hamiltonian at β=0∘ -- 12.7.2.2 Trough Solution: T1 ×Γ7: β≈100.893∘ -- 12.7.2.3 Trough Solution: T2 ×Γ6: β≈220.8934 -- References -- Epilogue -- A The Displaced Oscillator -- Contents -- A.1 Hamiltonian -- A.2 The Displacement Operator -- A.3 Eigenfunction of the Annihilation Operator -- A.4 Matrix Representation of the Displaced Oscillator -- References -- B Derivation of the Coupling Coefficients -- Contents -- B.1 Clebsch-Gordan Coupling Coefficients -- B.2 How to Calculate Coupling Coefficients -- B.3 Icosahedral States -- References -- C SU(n), SO(n), Sp(2n) Lie Algebras -- Contents -- C.1 The Special Unitary Group SU(n) -- C.2 The Special Orthogonal Group SO(n) -- C.3 The Symplectic Group Sp(2n) -- References -- D The Birkhoff Transformation -- Contents -- D.1 The Birkhoff Theorem -- D.2 Transformation of the Rabi Equation to the Standard Birkhoff Form -- D.3 Recursion Formulas for the Rabi Case -- D.4 Summary -- References -- E Dirac's Monopole -- Contents -- E.1 The Field of a Monopole -- E.2 The Vector Potential -- References -- F Yang's Monopole -- Contents -- F.1 Introduction -- F.2 The Tensor Potential A -- F.3 The Field Tensor F -- References. G Topological Graph Theory -- Contents -- G.1 Graphs -- G.2 Rings -- G.3 Faces -- References -- Compound Index -- Subject Index. |
| Record Nr. | UNISA-996490344903316 |
|
Ceulemans Arnout
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
The theory of the Jahn-Teller effect : when a boson meets a fermion / / Arnout Ceulemans
| The theory of the Jahn-Teller effect : when a boson meets a fermion / / Arnout Ceulemans |
| Autore | Ceulemans Arnout |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (429 pages) |
| Disciplina | 530.143 |
| Soggetto topico |
Interacting boson-fermion models
Jahn-Teller effect Efecte Jahn-Teller Bosons Fermions |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783031095283
9783031095276 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- Part I Bosons and Fermions -- 1 The Impossible Theorem -- Contents -- 1.1 The Jahn-Teller Theorem -- 1.2 Charge Density Analysis -- 1.2.1 Occupation of dz2 -- 1.2.2 Occupation of dx2-y2 -- 1.2.3 Sum and Difference Orbitals -- 1.2.4 Orthogonal and Unitary Combinations -- 1.3 Outlook -- References -- 2 Bosons and Fermions -- Contents -- 2.1 Bosons -- 2.1.1 The Schrödinger Formalism -- 2.1.2 The Dirac Formalism -- 2.1.3 The Bargmann Mapping -- 2.2 Fermions -- 2.2.1 Fermion Operators -- 2.2.2 One-Electron Interactions -- 2.2.3 Quasi-Spin -- References -- 3 Boson-Fermion Interactions -- Contents -- 3.1 The Jahn-Teller Effect in a Triangular Molecule: A Toy Model -- 3.1.1 The Hückel Hamiltonian -- 3.1.2 Fermions: Trigonal Molecular Orbitals -- 3.1.3 Bosons: Vibrational Modes -- 3.1.4 Coupling Coefficients -- 3.2 Degeneracies and Time Reversal -- 3.2.1 Time Reversal -- 3.2.2 Irreducible Representations of the First Kind and Orthogonal Lie Groups -- 3.2.3 Irreducible Representations of the Second Kind and Symplectic Lie Groups -- 3.2.4 Irreducible Representations of the Third Kind -- 3.3 The Jahn-Teller Hamiltonian -- 3.4 Selection Rules -- 3.4.1 Space Symmetry -- 3.4.2 Time Reversal Symmetry -- 3.4.3 Hole-Particle Exchange Symmetry -- 3.5 Proof of the Jahn-Teller Theorem -- 3.5.1 History -- 3.5.2 Where Do Degeneracies Come From? -- 3.5.2.1 Cosets and the Positional Representation -- 3.5.2.2 Doubly Transitive Orbits -- 3.5.3 Degenerate Representations and Jahn-Teller Modes -- 3.5.4 Jahn-Teller Activity in Simplexes -- References -- Part II Dynamic Symmetries -- 4 The Rabi Hamiltonian -- Contents -- 4.1 The Adiabatic Potential -- 4.2 The Quantum Model -- 4.3 Bargmann Mapping of the Wave Equations -- 4.4 Eigenvalues -- 4.4.1 Classification of the Roots -- 4.4.2 Recurrence Relations and Transcendental Function.
4.4.3 The Rabi Spectrum -- 4.5 The Quantization of the Rabi Hamiltonian -- 4.6 Analyticity -- 4.7 Inversion Tunneling in Ammonia -- References -- 5 The E ×e Orbital Doublet -- Contents -- 5.1 The Quantum Model -- 5.2 Dynamic Symmetries -- 5.2.1 Boson Symmetry -- 5.2.2 Fermion Symmetry -- 5.2.3 Coupled Symmetries -- 5.3 The Canonical Form of the Wave Equation -- 5.4 Recurrence Relationships -- 5.5 Results -- 5.6 Discussion -- 5.7 Application: Na3 and the (E+A)×e Hamiltonian -- References -- 6 The Spin Quartet Γ8 ×(e+t2) System and the Symplectic Group Sp(4) -- Contents -- 6.1 Historical Note: Judd and Reik -- 6.2 The Hamiltonian -- 6.2.1 The Static Case -- 6.2.2 The Dynamic Hamiltonian -- 6.3 Sp(4) Fermion Symmetry -- 6.4 SO(5) Boson Symmetry -- 6.5 The Γ8 ×(e+t2) Dynamic Equations -- 6.6 The Γ8 ×t2 Subsystem -- 6.6.1 SO(3) Invariance -- 6.6.2 Dynamic Equations -- 6.7 Application -- 6.7.1 ReF6 -- 6.7.2 IrF6 -- References -- 7 Ansatz for the Jahn-Teller Triplet Instability -- Contents -- 7.1 SO(5) Symmetry and the Five-Dimensional Harmonic Oscillator -- 7.1.1 SU(5) ↓ SO(5) Symmetry Breaking -- 7.1.2 SO(5) ↓ SO(3) Symmetry Breaking -- 7.2 The Hamiltonian -- 7.3 The Vibrating Sphere -- 7.4 Boson Functions -- 7.4.1 S States -- 7.4.2 D States -- 7.4.3 F States -- 7.5 The Ansatz -- 7.6 The Jahn-Teller Equations -- 7.7 Solution -- 7.8 Ansatz for Vibronic D States -- 7.9 Application -- 7.10 Conclusion -- References -- 8 The Icosahedral Quartet and SO(9) ↓ SO(4) Symmetry Breaking -- Contents -- 8.1 Introduction -- 8.2 Preamble: Hyperspherical Symmetry -- 8.3 The Hamiltonian -- 8.4 The Vibrations of the Four-Dimensional Hypersphere -- 8.5 SO(9) ↓ SO(4) Symmetry Breaking -- 8.5.1 (0,0) Modes -- 8.5.2 (1,1) Boson Modes -- 8.5.3 Modes with Seniority ν> -- 4 -- 8.6 The Ansatz: Vibronic (12,12) Levels -- 8.7 Icosahedral Symmetry Lowering. 8.8 Application: C20 and C80 Fullerenes -- 8.8.1 C20 -- 8.8.2 C80 -- References -- 9 SO(14) ↓ SO(5) Symmetry Breaking and the Jahn-Teller Quintet Instability -- Contents -- 9.1 Dynamic Symmetries -- 9.2 Descent to Spherical Symmetry -- 9.2.1 Branching Rules for SO(5) SO(3) -- 9.2.2 The L=2 Case -- 9.2.3 The L=4 Case -- 9.3 Descent to Permutational Symmetry -- 9.3.1 The Icosahedral Hamiltonian -- 9.3.2 The Hexateron -- 9.4 Correlation Between the Spherical and the Permutational Scheme -- 9.5 Application: The Ground State of C60+ Cation -- References -- 10 Jahn's and Teller's Last Case: The Spinor Sextet -- Contents -- 10.1 Group Theory of the Sextet Spinor -- 10.1.1 The Unitary Symplectic Group USp(6) -- 10.1.2 The SO(14) Group of the Bosons -- 10.2 The Γ9 ×(g+2h) Problem -- 10.2.1 The Hamiltonian -- 10.2.2 Diagonalization -- 10.2.3 The Equal Coupling Case -- 10.3 Chemical Applications -- 10.4 Overview -- 10.4.1 Orbital Representations: SO(N) ⊃ SO(n) -- 10.4.2 Spinor Representations: SO(N) ⊃ USp(2n) -- References -- Part III Topography -- 11 Conical Intersections and Quantum Fields -- Contents -- 11.1 The Berry Phase -- 11.1.1 The Quantal Phase Factor Accompanying Adiabatic Changes -- 11.1.1.1 Single-Valued Basis Functions -- 11.1.1.2 Real Basis Sets -- 11.1.2 Holonomy -- 11.2 The E×e Jahn-Teller Case -- 11.2.1 Berry Phase for the E×e Case -- 11.2.2 The Dirac Monopole Analogy -- 11.2.3 Berry Phase and Angular Momentum -- 11.3 Quadruple Spin Degeneracy and the Instanton -- 11.3.1 The Γ8 ×t2g Hamiltonian -- 11.3.2 The Γ8 ×(eg+t2g) Hamiltonian -- References -- 12 Topography and Chemical Reactivity -- Contents -- 12.1 Tools -- 12.1.1 The Epikernel Principle -- 12.1.2 The Isostationary Function -- 12.1.3 Proof of the Epikernel Principle -- 12.1.3.1 Only One Λ Irrep -- 12.1.3.2 More than One Λ Irrep -- 12.1.3.3 Illustration: The Γ×(Λ1+Λ2) Problem. 12.2 Orbital Doublets -- 12.2.1 The E×(b1+b2) System -- 12.2.2 The E×e System -- 12.2.3 The Pentagonal E1×e2 Problem -- 12.3 The Cubic T×(e+t2) Problem -- 12.3.1 Second-Order Warping Terms -- 12.3.2 Chemical Reactivity: The Isomerization of Fe(CO)4 -- 12.4 The Icosahedral T ×h System -- 12.5 The Icosahedral G×g+h Quartet System -- 12.5.1 The Isostationary Function -- 12.5.2 Tetrahedral Minima -- 12.5.3 Trigonal Minima -- 12.6 The Icosahedral H×(g+2h) Quintet System -- 12.6.1 The Isostationary Function -- 12.6.2 Pentagonal Minima -- 12.6.3 Trigonal Minima -- 12.7 The Icosahedral Γ9 ×(g+2h) Sextet System -- 12.7.1 The G-Type Subspace -- 12.7.2 The H Subspace -- 12.7.2.1 The FH2 Hamiltonian at β=0∘ -- 12.7.2.2 Trough Solution: T1 ×Γ7: β≈100.893∘ -- 12.7.2.3 Trough Solution: T2 ×Γ6: β≈220.8934 -- References -- Epilogue -- A The Displaced Oscillator -- Contents -- A.1 Hamiltonian -- A.2 The Displacement Operator -- A.3 Eigenfunction of the Annihilation Operator -- A.4 Matrix Representation of the Displaced Oscillator -- References -- B Derivation of the Coupling Coefficients -- Contents -- B.1 Clebsch-Gordan Coupling Coefficients -- B.2 How to Calculate Coupling Coefficients -- B.3 Icosahedral States -- References -- C SU(n), SO(n), Sp(2n) Lie Algebras -- Contents -- C.1 The Special Unitary Group SU(n) -- C.2 The Special Orthogonal Group SO(n) -- C.3 The Symplectic Group Sp(2n) -- References -- D The Birkhoff Transformation -- Contents -- D.1 The Birkhoff Theorem -- D.2 Transformation of the Rabi Equation to the Standard Birkhoff Form -- D.3 Recursion Formulas for the Rabi Case -- D.4 Summary -- References -- E Dirac's Monopole -- Contents -- E.1 The Field of a Monopole -- E.2 The Vector Potential -- References -- F Yang's Monopole -- Contents -- F.1 Introduction -- F.2 The Tensor Potential A -- F.3 The Field Tensor F -- References. G Topological Graph Theory -- Contents -- G.1 Graphs -- G.2 Rings -- G.3 Faces -- References -- Compound Index -- Subject Index. |
| Record Nr. | UNINA-9910616384203321 |
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Ceulemans Arnout
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| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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