TELEPARALLEL THEORY OF GRAVITATION: GRAVITOELECTROMAGNETISM, QUANTIZATION, AND SCATTERING UP TO ONE LOOP ORDER - MING (NIM : 30212016), KIAN
Gravitation has been an interesting subject among many years. Since the era of Albert Einstein and his theory of general relativity until quantum gravity theory, various discussions, developments, and models keep emerging. One of the great ideas is how gravitational field interacts with matter fields (scalar, spinor, and vector fields). In order to find such interactions between gravitational field and others matter fields, we have to place gravitational theory and gauge theory, which successfully explain the others three interactions, in the same framework. Combining the two theories which have different basic formulations is a giant work that has yet been finished. This giant work is called the quantum gravity theory. So far, however, the theory is still far from established. Teleparallel gravity is an equivalent theory of general relativity. Even though they differ in formulations they are equivalent as their Lagrangian are equivalent up to a surface term. Therefore, teleparallel gravity can be viewed as an option for a gauge theory for gravitation giving a great opportunity to answer the difficulties of quantum gravity. This research considers weak field approximation and define tetrads as , where as the coupling constant and as the gravity field. The similarity between NewtonÃ‚Â’s gravitational force and electric force raises a new idea to formulate gravitation. This idea is known as gravitoelectromagnetism (GEM). The aim of this idea is to express the gravitational theory in a similar form with the electromagnetism theory. This similarity is obtained by deriving four Maxwell-like equations from the gravitational theory. Hopefully GEM formulation can explain various phenomena which have or have not been be explained by general relativity. GEM formulation for teleparallel gravity prior to this research was incomplete, namely, the full set of Maxwell-like equations was not able to derive. With this research, we are able to to formulate a full set of Maxwell-like equations for teleparallel gravity. Here we define the torsion as the gravitational field strength consisting of gravitoelectric and gravitomagnetic fields and weak field approximation is taken into account. We then apply the results to Schwarzschild metric and gravitational waves in order to obtain the gravitoelectric and gravitomagnetic fields as well as scalar and vector potentials for these two space-times.In addition, Poynting vectors are obtained from stress tensors using teleparallel lagrangian. In the case of gravitational waves, the Poynting vector reveals energy transfer in the tangent space and curved space. Quantization is a great problem in gravitational theory. Among the four fundamental interactions, gravity is only non-quantized fields. Teleparallel gravity as the gauge theory for gravitation may answer this problem. We consider canonical quantization and path integral quantization for teleparallel gravity. We could derive canonical quantization even though not in a simple and consistent results. Generating functional can be obtained using path integral quantization methods where as the quantized objects. By obtaining generating functional the condition of quantized gauge fields are fulfilled. Then, the propagator of free gravitational field is obtained from the gravitational generating functional using second order Green's functions. Scattering processes can express the interaction between gravitational fields with scalar and vector fields. Interaction prescription is contained inside covariant derivative like in gauge theory. Feynman rules for scalar-gravity interactions and vector-gravity interactions are obtained from scalar field and vector field lagrangian coupled with gravitation. From these rules, the scattering amplitudes of several scattering process can be obtained, such as the Compton process and the graviton radiation. We obtain that scattering amplitudes for the lowest order of interactions (Feynman diagrams without any loops) are finite while those containing loops have either ultraviolet, infrared, or logarithmic divrgences. These divergences are similar to ultraviolet divergences from general relativity. Divergences seem an inherited property of general relativity and also teleparallel gravity as the equivalent theory of general relativity.