The Six-Dimensional World
  1. Quantum Field Theory
    1. Homogeneous spaces and internal quantum numbers

      2. In order to define relativistically invariant field functions, fields are defined as unitary irreducible representations of the Poincaré group. When the carrier space for these representations is taken to be ordinary Minkowski space-time, the resulting fields are spinors. It is possible, however, to obtain scalar-valued wave functions with non-trivial spin spectra by selecting as carrier space larger homogeneous spaces of the Poincaré group, Minkowski space being just such a homogeneous space of that group.

      In order to construct such fields with an isospin spectrum within this approach, it is necessary to consider unitary irreducible representations of groups larger than the Poincaré group but which include it as a subgroup.

    2. Deformable Elastic Sphere Model

      3. The quantum field theory developed in the previous paper is shown to correspond, in the non-relativistic limit, to a deformable elastic sphere model.

    3. Deformable Elastic Spheres as Generalized Strings

      4. It is shown how current String Theories are obtained as a limiting case of the Sphere Theory developed here.

    4. The Interpretation of the Added Dimensions

     

  2. The "Flatland" hypothesis
    1. 3-dimensional space of extension + 3-dimensional space of intension
    2. Verification and falsification
    3. Familiar three- and four-dimensional constructs in six-dimensional formulation
    4. Many-worlds interpretation re-interpreted?
    5. Causality as seen from four- and six-dimensions, respectively
    6. Causal and acausal connections
      1. Pauli's exclusion principle
      2. Jung and Pauli's synchronicity concept
      3. SU(6) Phenomenology

     

  3. Graphic visualizations of a six-dimensional world
    1. Two-dimensional representations of three-dimensional sections of six-dimensional objects
    2. Mathematical Duality

     

  4. The indefinite metric of SO(3,3)
    1. A side-issue : "compactification"
    2. (Jordan curves and the Jordan-Schoenflies theorem)
    3. Making distinctions
    4. Structures and objects in intensional subspace
      1. Categories and archetypes
      2. Form enhancing distance distortion