Ivancevic_Applied-Diff-Geom

702 Applied Differential Geometry: A Modern Introductiongravity (see [Rovelli (1998)] and references therein). The first announcementof this approach was given in [Rovelli and Smolin (1987)]. Togetherwith string theory, this approach provides another serious candidate theoryof quantum gravity. It provides a physical picture of Planck scale quantumgeometry, calculation techniques, definite quantitative predictions, and atool for discussing classical problems such as black hole thermodynamics.String theory and loop quantum gravity differ not only because theyexplore distinct physical hypotheses, but also because they are expressionsof two separate communities of scientists, which have sharply distinct prejudices,and view the problem of quantum gravity in surprisingly differentmanners. As Rovelli says: “I heard the following criticism to loop quantumgravity: ‘Loop quantum gravity is certainly physically wrong, because:(1) it is not supersymmetric, and(2) is formulated in four dimensions’.But experimentally, the world still insists on looking four–dimensional andnot supersymmetric. In my opinion, people should be careful of not beingblinded by their own speculation, and mistaken interesting hypotheses(such as supersymmetry and high–dimensions) for established truth. Butstring theory may claim extremely remarkable theoretical successes and istoday the leading and most widely investigated candidate theory of quantumgravity” [Rovelli (1998)].High energy physics has obtained spectacular successes during this Century,culminated with the (far from linear) establishment of quantum fieldtheory as the general form of dynamics and with the comprehensive successof the SU(3) × SU(2) × U(1) Standard Model. Thanks to this success,now a few decades old, physics is in a condition in which it has been veryrarely: there are no experimental results that clearly challenge, or clearlyescape, the present fundamental theory of the world. The theory we haveencompasses virtually everything – except gravitational phenomena. Fromthe point of view of a particle physicist, gravity is then simply the last andweakest of the interactions. It is natural to try to understand its quantumproperties using the strategy that has been so successful for the restof microphysics, or variants of this strategy. The search for a conventionalquantum field theory capable of embracing gravity has spanned severaldecades and, through an adventurous sequence of twists, moments of excitementand disappointments, has lead to string theory. The foundationsof string theory are not yet well understood; and it is not yet entirely clearhow a supersymmetric theory in 10 or 11 dimensions can be concretely used