Conformal Groups and Related Symmetries Physical Results and Mathematical Background [electronic resource] : Proceedings of a Symposium Held at the Arnold Sommerfeld Institute for Mathematical Physics (ASI) Technical University of Clausthal, Germany August 12–14, 1985 / edited by A. O. Barut, H. -D. Doebner.

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 the Virasoro, 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.