2 Elementary systems on G-manifolds. 292 3 Two elementary systems: The(G×G)-manifold and its subma- fold splitting underdiag(G×G). 293 4 Examples of internal coordinates on(G×G). 297 5 Kronecker products and two-particle state decompositions on(G× G). 298 6 Fusion of two elementary systems on(G×G). 300 7 Elementary systems on the Poincare-manifold. ¿ 301 7. 1 Mackey and covariant ?elds. 301 7. 2 From covariant to Mackey ?elds. 302 7. 3 Obstruction of Poincare-manifolds ¿ by covariant ?elds. 303 8 Relativistic position operators and coordinates. 305 8. 1 Position operators for relativistic Mackey ?elds. 305 8. 2 Position operators for ?elds with spin. 306 9 From Dirac ?elds to Bargmann-Wigner ?elds by fusion. 307 10 Elementary systems in interaction. 309 10. 1 Euclidean invariant interactions. 309 10. 2 Interacting Dirac spinor ?elds. 310 11 Scission of an elementary system. 311 12 Conclusion. 313 13 Appendix. 313 13. 1 A: Orthogonality and completeness of unitary represen- tions. 313 13. 2 B: Parameters, cosets and multiplication rules forSl(2,C). 313 13. 3 C: Observables in the relativistic 2-body system. 314 Propagation in crossed electric and magnetic ?elds 317 T. Kramer, C. Bracher 1 Introduction 317 2 Elastic scattering and quantum sources 318 2. 1 Connection to the propagator 319 2. 2 Currents generated by quantum sources 321 2. 3 Density of States 322 2. 4 Construction of the Green function 322 3 Matter waves in crossed electric and magnetic ?elds 324 3. 1 The quantum propagator 324 3.

Why Symmetry?.- J-Pairing Interractions of Fermions in a Single-J Shell.- Supersymmetry in Nuclei.- The Relativistic Many Body Problem in Quantum Mechanics.- Gauge Invariance and the E1 Sum Rule in Nuclei.- The Heisenberg Group in Classical and Quantum Information Transmission.- Quantum Field Theory of Particle Mixing and Oscillations.- Two-Photon Interactions in Cavity QED.- Low-Dimensional Spin Systems: Hidden Symmetries, Conformal Field Theories and Numerical Checks.- Quantum Tomography, Wave Packets and Solitons.- Borel Quantization and Nonlinear Quantum Mechanics.- Seeing Science through Symmetry.- Space-Time Symmetries on Clifford Algebra C4 Based Representation Spaces of su(4) ? so(6).- Fermionic O(8) and Bosonic U(36) Symmetry Schemes for Heavy N=Z Nuclei.- Interaction and Fusion of Elementary Systems.- Propagation in Crossed Electric and Magnetic Fields: The Quantum Source Approach.- On Group Theoretical Aspects, Hypergeometric Transformations and Symmetries of Angular Momentum Coefficients.- Tensor and Spin Representations of SO(4) and Discrete Quantum Gravity.- The Geometry of Density States, Positive Maps and Tomograms.- Objective Existence and Relativity Groups.- Survival of Quasi-Spin Structure in Isomers of N ? 82 Nuclei.- Irreversible Wave Packet Dynamics in a Magnetic Field.- From Quantum Groups to Genetic Mutations.- Noncompact Quantum Algebra Uq(2,1): Positive Discrete Series of Irreducible Representations.- Combinatorial Physics, Normal Order and Model Feynman Graphs.- Bohr¿s Symmetry and the Quantum Numbers for the Triaxially Superdeformed Bands in Odd Mass Nuclei.- Understanding Brain and Consciousness?.- Beta-Decay in Odd-A Cs to Xe in the Interacting Boson-Fermion Model.- Triaxiality and Chirality in Nuclei Around Mass 130.