Reduction of Standard Model Structure to CP2 Geometry and Other Key Ideas of TGD

Abstract

Originally this article was an appendix meant to be a purely technical summary of basic facts but in its recent form it tries to briefly summarize those basic visions about TGD which I dare to regard as stabilized. I have added illustrations making it easier to build mental images about what is involved and represented briefly the key arguments. This chapter is hoped to help the reader to get fast grasp about the concepts of TGD. The basic properties of embedding space and related spaces are discussed and the relationship of CP₂ to the standard model is summarized. The basic vision is simple: the geometry of the embedding space H = M⁴ x CP₂ geometrizes standard model symmetries and quantum numbers. The assumption that space-time surfaces are basic objects, brings in dynamics as dynamics of 3-D surfaces based on the induced geometry. Second quantization of free spinor fields of $H$ induces quantization at the level of H, which means a dramatic simplification. The notions of induction of metric and spinor connection, and of spinor structure are discussed. Many-sheeted space-time and related notions such as topological field quantization and the relationship many-sheeted space-time to that of GRT space-time are discussed as well as the recent view about induced spinor fields and the emergence of fermionic strings. Also the relationship to string models is discussed briefly. Physics as number theory is complementary to physics as geometry vision in TGD. All basic number fields, including finite fields, rationals and their extensions, p-adic number fields and their extensions and also complex numbers, quaternions and octonions are central for this vision. p-Adic length scale hypothesis and hierarchy of Planck constants labelling phases of ordinary matter behaving like dark matter are basic applications. Zero energy ontology (ZEO) has become a central part of quantum TGD and leads to a TGD inspired theory of consciousness as a generalization of quantum measurement theory having quantum biology as an application. Also these aspects of TGD are briefly discussed.