Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1999-10-17
J.Math.Phys. 41 (2000) 3776-3800
Physics
High Energy Physics
High Energy Physics - Theory
To appear in the Journal of Mathematical Physics 2000 Special Issue
Scientific paper
10.1063/1.533327
In fundamental physics, this has been the century of quantum mechanics and general relativity. It has also been the century of the long search for a conceptual framework capable of embracing the astonishing features of the world that have been revealed by these two ``first pieces of a conceptual revolution''. I discuss the general requirements on the mathematics and some specific developments towards the construction of such a framework. Examples of covariant constructions of (simple) generally relativistic quantum field theories have been obtained as topological quantum field theories, in nonperturbative zero-dimensional string theory and its higher dimensional generalizations, and as spin foam models. A canonical construction of a general relativistic quantum field theory is provided by loop quantum gravity. Remarkably, all these diverse approaches have turn out to be related, suggesting an intriguing general picture of general relativistic quantum physics.
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