Conformal Groups and Related Symmetries Physical Results and Mathematical Background

Inhaltsverzeichnis

• 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.