Quantum Gravity (QG) is a very interesting and challenging subject in Physics. Physicists use many different approaches to study QG. This dissertation uses the conventional perturbation method since other approaches have not been proven to produce fruitful results. In the conventional perturbation theory, there are two problems in QG, namely, ultraviolet and infrared singularities. The latter is the subject of this dissertation. The oldest way to treat infrared singularity is to use momentum cutoff. In any scattering process, a lower momentum cutoff is used in calculating 1-loop or higher order diagrams. Then, another cutoff is used in calculating diagrams with soft graviton emission. Physical cross-section is obtained by summing these contributions. It can be shown that the cross-section depends on the ratio of cutoffs. As there is no prior reason that the cutoffs should be the same, there is ambiguity in this approach. The better alternative, which was invented by Feynman in the context of QED, attributed a small mass for photon. This procedure eliminates the ambiguity as the mass should be used in all calculations. The same advantage should exist if this procedure is being applied to QG. An explicit calculation of a particular physical process with both methods, using momentum cutoffs and introducing mass, to treat the infrared singularity is shown and the results are compared. The ambiguity of the former procedure is explicitly seen. An internally consistent theory of massive gravity is being investigated. The mass of graviton should be introduced in a smooth manner so that the theory is free of singularities in the massless limit. The number of degrees of freedom should also be preserved. A formulation with this property exists, and it involves massive graviton and two other fields, all the fields are free. There are two local symmetries in this theory. The interaction among the fields is studied. The two local symmetries imply two identities for free field equations. Through the free field equations, conditions of consistency are imposed for having a good perturbation theory. With these constraints, a physically unique interaction can be constructed. However, in this interaction, the coupling of gravity to other fields is half of the self coupling of gravity. It indicates that the equivalence principle is being violated. An antisymmetric field is being added to the formulation in order to solve this problem. However, promising results have not been obtained yet. We hope that further researches can be conducted to investigate along this direction, with or without other fields. Thus, a consistent massive theory of gravitation can be constructed. Moreover, solving the infrared problem may shed some light on the issue of ultraviolet singularity, just like the case of electroweak theory. Hopefully, a complete quantum theory of gravity can be constructed through this process. Thus, massive theory of Quantum Gravity would be an exciting subject.
- Pub Date:
- January 1995
- Physics: Elementary Particles and High Energy, Physics: Astronomy and Astrophysics