Aside from the obvious statement that it should be a theory
capable of unifying general relativity and quantum field theory,
not much is known about the true nature of quantum gravity.
New ideas - and there are many of them for this is an exciting
field of research - often diverge to a degree where it seems
impossible to decide in which of the many possible direction(s) the
ongoing developments should be further sustained.
The division of the book in two (overlapping) parts reflects the
duality between the physical vision and the mathematical
construction. The former is represented by tutorial reviews on
non-commutative geometry, on space-time discretization and
renormalization and on gauge field path integrals. The latter one
by lectures on cohomology, on stochastic geometry and on
mathematical tools for the effective action in quantum gravity.
The book will benefit everyone working or entering the field of
quantum gravity research.
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