Integration of General Relativity and Quantum Theory: Octonion Cosmology, GiFT, Creation/Annihilation Spaces CASe, Reduction of Spaces to a Few Fermions and Symmetries in Fundamental Frames

The particles that we see generally depend on the coordinate system. The spatial/time measurements that we make depend on particles - an intimate connection that is often ignored in physical theories. This book explores the relation between particles and coordinate systems. It shows that a transformation to a non-static coordinate system from a "normal" static coordinate system can change the nature of the particle spectrum decisively. (Since almost all coordinates systems are non-static it is a weighty issue.)

The book begins by describing the changes undergone by creation/annihilation operators in quantum fields due to a change to non-static coordinates. It then proceeds to develop a new concept of space based on the Generalized Field Theory (GiFT) called Creation/Annihilation Space (CASe). CASe transformations to a non-static reference frame, which we call a Fundamental Frame, can reduce complex quantum field theories such as QUeST in our universe to a field theory with only 16 fermions and three internal symmetries - a one generation Standard Model - in a non-static reference frame. In the other universes of Octonion Cosmology it is also possible to reduce the complexity of quantum field theories to much fewer fermions and internal symmetries.

This book explores the Fundamental Frame of our universe and of the other higher dimension universes of Octonion Cosmology in detail. It shows the contents of the universes of Octonion Cosmology can be contracted to smaller size. The formalism is strongly based on Cayley-Dickson hypercomplex numbers: octonions, sedenions, ..., n-ions, ... where an n-ion is a hypercomplex number of Cayley-Dickson number n.

An analysis of the nature of fermions shows that the four types of fermions: e-type, ν-type, quark-up-type, and quark-down-type, can be viewed as generated by Complex Lorenz group boosts. The author's 2007 book The Origin of the Standard Model ..., describing this in detail is reprinted for the reader's convenience. The fermions of Fundamental Frames are of these types.

Gravitation joins the other gauge theories of interactions in GiFT. It has a finite perturbation theory due to GiFT's Two-Tier Theory and PseudoQuantum Theory.