A quantum theory of gravitation is constructed, by considering the gravitational field in the linear approximation to be a rank II tensor field, which has imposed upon it the auxiliary conditions of symmetry, transversality, and tracelessness. Extensive use is made of the close analogy between the electromagnetic field as a special case of a vector field, and the gravitational field as a special case of a tensor field. This analogy includes the necessity of introducing an indefinite
metric in order to make the auxiliary conditions compatible with the commutation relations.
A complete theory of gravitation must take into account the gravitating nature of gravitation and hence must be a nonlinear
theory. A method proposed by Gupta of iterating the linear field equations for this purpose is investigated, and it is shown that this method fails, because the Lagrangian for the second order equations does not exist. An alternative method of iteration is proposed which avoids this problem, and which yields a functional equation for the Lagrangian of the full nonlinear theory.
Finally, the problem of photon-photon scattering due to the gravitational interaction is investigated. This is done by constructing an interaction Hamiltonian by using the principle
of the compensating field and then applying the standard methods of quantum electrodynamics. It is found that for
sufficiently high frequencies this process dominates the purely
electrodynamic scattering of photons by photons. / Science, Faculty of / Physics and Astronomy, Department of / Graduate
| Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/37758 |
| Date | January 1967 |
| Creators | Freeman, Michael James |
| Publisher | University of British Columbia |
| Source Sets | University of British Columbia |
| Language | English |
| Detected Language | English |
| Type | Text, Thesis/Dissertation |
| Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
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