03791nam 2200661 450 991045618870332120200520144314.01-282-04213-097866120421331-4426-7206-410.3138/9781442672062(CKB)2420000000003904(EBL)3258032(SSID)ssj0000290795(PQKBManifestationID)11225476(PQKBTitleCode)TC0000290795(PQKBWorkID)10230709(PQKB)11703639(CaBNvSL)thg00602294 (MiAaPQ)EBC3258032(MiAaPQ)EBC4671298(DE-B1597)464274(OCoLC)944178396(DE-B1597)9781442672062(Au-PeEL)EBL4671298(CaPaEBR)ebr11257016(OCoLC)244768864(EXLCZ)99242000000000390420160926h19991999 uy 0engur|n|---|||||txtccrCanadian annual review of politics and public affairs, 1993 /edited by David Leyton-BrownToronto, [Ontario] ;Buffalo, [New York] ;London, [England] :University of Toronto Press,1999.©19991 online resource (337 p.)Canadian Annual Review of Politics and Public AffairsIncludes index.0-8020-4701-7 Frontmatter -- Contents -- Contributors -- Acknowledgments -- Canadian calendar 1993 -- Editor's introduction - the year in review -- Parliament and politics -- Ottawa and the provinces -- External affairs and defence -- Ontario -- Quebec -- Nova Scotia -- New Brunswick -- Manitoba -- British Columbia -- Prince Edward Island -- Saskatchewan -- Alberta -- Newfoundland and Labrador -- Yukon and Northwest Territories -- Obituaries 1993 -- Index of names -- Index of subjects The year 1993 marked the changing of the political guard at both federal and provincial levels. While the cast of characters changed, however, the agendas remained much the same. Public policy was dominated by concerns about deficit and debt. Provincial governments faced declining tax revenues, which was exacerbated by reduced federal equalization payments and transfers. On the international front 1993 was the year that Parliament approved the North American Free Trade Agreement. Peacekeeping remained an important aspect of Canada's contribution to international security, but that contribution was sullied by the Somali affair. The resulting investigation affected all levels of the Department of National Defence.Featuring essays on Parliament and politics, Ottawa and the provinces, and external affairs and defence, the Canadian Annual Review of Politics and Public Affairs provides a comprehensive account of the year's events.The Canadian Annual Review has long been praised for its excellence. Known for its accuracy, readability, and insight, it offers a synoptic appraisal of the year's crises, controversies, and developments from both federal and provincial perspectives.POLITICAL SCIENCE / Public Affairs & AdministrationbisacshCanadaEconomic conditions1945-CanadaForeign relations1945-CanadaPolitics and government1945-Electronic books.POLITICAL SCIENCE / Public Affairs & Administration.330.971064Leyton-Brown DavidMiAaPQMiAaPQMiAaPQBOOK9910456188703321Canadian annual review of politics and public affairs, 19932479076UNINA09350nam 2200565 450 99649034490331620230727165155.09783031095283(electronic bk.)9783031095276(MiAaPQ)EBC7102390(Au-PeEL)EBL7102390(CKB)24950538500041(PPN)264960742(EXLCZ)992495053850004120230226d2022 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierThe theory of the Jahn-Teller effect when a boson meets a fermion /Arnout CeulemansCham, Switzerland :Springer,[2022]©20221 online resource (429 pages)Print version: Ceulemans, Arnout The Theory of the Jahn-Teller Effect Cham : Springer International Publishing AG,c2022 9783031095276 Includes bibliographical references and index.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&gt -- 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.Interacting boson-fermion modelsJahn-Teller effectEfecte Jahn-TellerthubBosonsthubFermionsthubLlibres electrònicsthubInteracting boson-fermion models.Jahn-Teller effect.Efecte Jahn-TellerBosonsFermions530.143Ceulemans Arnout1260221MiAaPQMiAaPQMiAaPQ996490344903316The Theory of the Jahn-Teller Effect2920193UNISA