5 Main Ideas and Physical Inputs 

The main physical hypotheses on which loop quantum gravity relies are only general relativity and quantum mechanics. In other words, loop quantum gravity is a rather conservative ``quantization'' of general relativity, with its traditional matter couplings. In this sense, it is very different from string theory, which is based on a strong physical hypothesis with no direct experimental support (the world is made by strings).

Of course ``quantization'' is far from a univocal algorithm, particularly for a nonlinear field theory. Rather, it is a poorly understood inverse problem (find a quantum theory with the given classical limit). More or less subtle choices are made in constructing the quantum theory. I discuss these choices below.

• 5.1 Quantum field theory on a differentiable manifold
• 5.2 One additional assumption
• 5.3 Physical meaning of diffeomorphism invariance, and its implementation in the quantum theory
• 5.4 Problems not addressed

Loop Quantum Gravity Carlo Rovelli http://www.livingreviews.org/lrr-1998-1 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de