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
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
Part IV: The first chapter summarizes the basic ideas related to von Neumann algebras known as hyper-finite factors of type II1 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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