Three Roads To Quantum Gravity

SUGGESTIONS FOR FURTHER READING
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9808070. The reformulation of the consistent histories formulation in
terms of topos theory, which emphasizes its relational aspects, is found
in C.J. Isham and J. Butter®eld, `Some possible roles for topos theory in
quantum theory and quantum gravity', gr-qc/9910005. Other relational
approaches to quantum cosmology are found in L. Crane, Journal of
Mathematical Physics 36 (1995) 6180; L. Crane, in Knots and Quantum
Gravity, edited by J. Baez (Oxford University Press, New York, 1994);
L. Crane, `Categorical physics', hep-th/9301061; F. Markopoulou, `Quantum
causal histories', hep-th/9904009, Class. Quan. Grav. 17 (2000)
2059±2072; F. Markopoulou, `An insider's guide to quantum causal
histories', hep-th/9912137, Nucl. Phys. Proc. Suppl. 88 (2000) 308±313;
C. Rovelli, `Relational quantum mechanics', quant-ph/9609002, International
Journal of Theoretical Physics 35 (1996) 1637; L. Smolin, `The
Bekenstein bound, topological ®eld theory and pluralistic quantum
cosmology', gr-qc/950806.
CHAPTER 4
The process formulation of quantum theory was developed ®rst by
David Finkelstein, whose work is the main inspiration for this chapter.
It is described in David Ritz Finkelstein, Quantum Relativity: A
Synthesis of the ideas of Einstein and Heisenberg (Springer-Verlag,
1996). Rafael Sorkin has also pioneered the exploration of the role of
causality in quantum gravity.
CHAPTERS 5±8
This is all standard material in classical general relativity and quantum
®eld theory. Good introductions are N.D. Birrell and P.C.W. Davies,
Quantum Fields in Curved Spacetime (Cambridge University Press,
1982); and Robert M. Wald, Quantum Field Theory in Curved Spacetime
and Black Hole Thermodynamics (University of Chicago Press,
1994).
CHAPTERS 9 AND 10
There are several expositions of loop quantum gravity at a semipopular
or semi-technical level. They include Carlo Rovelli, `Loop
quantum gravity', gr-qc/9710008, Carlo Rovelli, `Quantum spacetime:
what do we know?', gr-qc/9903045; L. Smolin in Quantum Gravity
and Cosmology, edited by Juan Perez-Mercader et al. (World Scienti®c,
1992); L. Smolin, `The future of spin networks', in The Geometric
Universe (1997), edited by S.A. Huggett et al. (Oxford University
Press, 1998), gr-qc/9702030. The book by Rodolfo Gambini and Jorge
Pullin, Loops, Knots, Gauge Theories and Quantum Gravity (Cambridge
University Press, 1996) describes their approach to the subject.