This book, as well as earlier books, broadens theoretical efforts with new concepts and ideas due to Octonion Cosmology.

To that end it develops a deeper basis for Quantum Theory. The new basis is required by the higher dimension universes that appear in Octonion Cosmology ranging up to 20 space-time dimensions. As a result Quantum Theory requires a new formulation of Field Theory: the author’s solution is a Generalized Field Theory (GiFT), which leads ultimately to Quantum Mechanics in a series of stages with each dependent on the previous:

Origin: Generalized Field Theory (GiFT)

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Quantum Field Theory

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Quantum Mechanics

Quantum Mechanics issues are resolved by Quantum Field Theory or ultimately by GiFT.

The book develops an Extended Quantum Mechanics that combines quantum and classical mechanics with each being a limiting case of the extended theory. Extended Quantum Mechanics is the Quantum Mechanical equivalent of PseudoQuantum Field Theory, a part of GiFT.

GiFT is based on Two-Tier Quantum Theory and PseudoQuantum Field Theory, both of which the author developed some time ago. They resolve divergence problems, and also non-static coordinate system quantization issues, that appear in higher dimension universes. Four dimension renormalization methods do not work in higher dimensions. Particle quantization has difficulties in non-static coordinate systems with no Killing vector. GiFT resolves those difficulties. GiFT contains a local SU(1, 1) group structure that gives a new interpretation to creation/annihilation operators in field theory.

The extended Quantum Mechanics version of GiFT is CQ Mechanics - a Quantum Mechanics that also embodies a classical mechanics limit. It appears in appendix C.

The Octonion Universes Spectrum is closely related to spinor arrays. We have shown spinor arrays have a similar block structure to hypercomplex numbers, which, in turn, are closely related to the structure of internal symmetry groups. In this book we derive the Octonion Cosmology Spectrum of universes partly based on spinor array features.

Lastly, QED-like interactions in higher dimension universes are considered including the EM potential and Bohr-like atomic energy levels. It suggests our kind of Life is unlikely in higher dimension universes.