Conformal Groups and Related Symmetries Physical Results and Mathematical Background

From Heisenberg algebra to conformal dynamical group.- $$overline {SL}$$ (4,R) dynamical symmetry for hadrons.- A new quantum relativistic oscillator and the hadron mass spectrum.- Path integral realization of a dynamical group.- Polynomial identities associated with dynamical symmetries.- De - sitter representations and the particle concept, studied in an ur-theoretical cosmological model.- The structure of local algebras in quantum field theory.- Does supergravity allow a positive cosmological constant.- Photons and gravitons in conformal field theory.- On conformally covariant energy momentum tensor and vacuum solutions.- The holonomy operator in Yang-Mills theory.- Conformal geodesics.- Second order conformal structures.- The conformal structure of Einstein's field equations.- Nonrelativistic conformal symetries and Bargmann structures.- Wave equations for conformal multispinors.- Global conformal transformations of spinor fields.- Pure spinors for conformal extensions of space-time.- Complex Clifford analysis over the Lie ball.- Plancherel theorem for the universal cover of the conformal group.- Harmonic analysis on rank one symmetric spaces.- A spin-off from highest weight representations; conformal covariants, in particular for 0(3,2).- Tensor calculus in enveloping algebras.- Representations of the Lorentz Algebra on the space of its universal enveloping algebra.- Reducible representations of the extended conformal superalgebra and invariant differential operators.- All positive energy unitary irreducible representations of the extended conformal superalgebra.- The two-dimensional quantum conformal group, strings and lattices.- Finite-size scaling and irreducible representations of virasoro algebras.- Unitarizable highest weight representations of theVirasoro, Neveu-Schwarz and Ramond algebras.- Structure of Kac-Moody groups.- Infinite dimensional lie algebras connected with the four-dimensional laplace operator.- Infinite dimensional lie algebras in conformal QFT models.