Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1999-01-17
Adv.Theor.Math.Phys. 3 (1999) 1289-1324
Physics
High Energy Physics
High Energy Physics - Theory
26 pages, Revtex; minor changes
Scientific paper
It is well known that, in the first-order formalism, pure three-dimensional gravity is just the BF theory. Similarly, four-dimensional general relativity can be formulated as BF theory with an additional constraint term added to the Lagrangian. In this paper we show that the same is true also for higher-dimensional Einstein gravity: in any dimension gravity can be described as a constrained BF theory. Moreover, in any dimension these constraints are quadratic in the B field. After describing in details the structure of these constraints, we scketch the ``spin foam'' quantization of these theories, which proves to be quite similar to the spin foam quantization of general relativity in three and four dimensions. In particular, in any dimension, we solve the quantum constraints and find the so-called simple representations and intertwiners. These exhibit a simple and beautiful structure that is common to all dimensions.
Freidel Laurent
Krasnov Kirill
Puzio Raymond
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