**Authors:** Matti Pitkänen

This book tries to give an overall view about quantum TGD as it stands now. The topics of this book are following.

- Part I: An overall view about the evolution of TGD and about quantum TGD in its recent form. Two visions about physics are discussed at general level. According to first vision physical states of the Universe correspond to classical spinor fields in the world of the classical worlds (WCW) identified as 3-surfaces or equivalently as corresponding 4-surfaces analogous to Bohr orbits and identified as special extrema of Kähler action. TGD as a generalized number theory vision leading naturally also to the emergence of p-adic physics as physics of cognitive representations is the second vision.
- Part II: The vision about physics as infinite-dimensional configuration space geometry. The basic idea is that classical spinor fields in WCW describe the quantum states of the Universe. Quantum jump remains the only purely quantal aspect of quantum theory in this approach since there is no quantization at the level of the configuration space. Space-time surfaces correspond to special extremals of the Kähler action analogous to Bohr orbits and define what might be called classical TGD discussed in the first chapter. The construction of the configuration space geometry and spinor structure are discussed in remaining chapters.
- Part III: Physics as generalized number theory. Number theoretical vision involves three loosely related approaches: fusion of real and various p-adic physics to a larger whole as algebraic continuations of what might be called rational physics; space-time as a hyper-quaternionic surface of hyper-octonion space, and space-time surfaces as a representations of infinite primes.
- Part IV: The first chapter summarizes the basic ideas related to von Neumann algebras known as hyper-finite factors of type II
_{1}about which configuration space Clifford algebra represents canonical example. Second chapter is devoted to the basic ideas related to the hierarchy of Planck constants and related generalization of the notion of imbedding space to a book like structure. - Part V: Physical applications of TGD. Cosmological and astrophysical applications are summarized and applications to elementary particle physics are discussed at the general level. TGD explains particle families in terms of generation-genus correspondence (particle families correspond to 2-dimensional topologies labeled by genus). The general theory for particle massivation based on p-adic thermodynamics is discussed at the general level.

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