Theory of the Jahn-Teller Effect

Part I: BOSONS AND FERMIONS.- The Impossible Theorem.- Bosons and Fermions.- Boson-Fermion Interactions.- PART II: DYNAMIC SYMMETRIES.- The Rabi Hamiltonian.- The E x e Orbital Doublet.- The Spin Quartet ? 8 x (e + t2) System and the Symplectic Group Sp(4).- Ansatz for the Jahn-Teller Triplet Instability.- The Icosahedral Quartet and SO(9) SO(4) Symmetry Breaking.- SO(14) SO(5) Symmetry Breaking and the Jahn-Teller Quintet Instability.- Jahn's and Teller's Last Case: the Spinor Sextet.- PART III: TOPOGRAPHY.- Conical Intersections and Quantum Fields.- Topography and Chemical Reactivity.- Epilogue.- APPENDICES.- Appendix A The Displaced Oscillator.- Appendix B Derivation of the Coupling Coefficients.- Appendix C SU(n), SO(n), Sp(2n) Lie Algebras.- Appendix D The Birkhoff Transformation.- Appendix E Dirac's Monopole.- Appendix F Yang's Monopole.- Appendix G Topological Graph Theory.

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Jahn-Teller effect;Vibronic coupling;boson-fermion interaction;Bargmann-Fock representation;Mexican hat potential;Rabi Hamiltonian;Symmetry breaking;Lie groups;Molecular symmetry groups;Icosahedral symmetry