THE INTERACTION PICTURE IN GRAVITATIONAL THEORY
A quantized version of the Einstein theory of gravitation is considered in which the De Donder coordinate conditions, as formulated by Fock, are imposed as auxiliary conditions on the state vectors. These conditions are not generally covariant in form. The quantization is made possible, as in Fermi's form of quantum electrodynamics, by the addition of some terms to the original Lagrangian which are to vanish on account of the auxiliary condition. The conjecture of Fock that the De Donder-Fock coordinate conditions determine the coordinate system up to a Lorentz transformation is used to formulate the theory in a Lorentz-covariant way. For this purpose, a flat-space (Minkowski) metric gamma / sub u nu / is introduced in addition to the physical metric g/sub u nu /. The unitary transformation between the Heisenberg picture and the interaction picture is determined by the TomonagaSchwinger equation which is only defined for a certain class of spacelike surfaces. It is shown that the equation is integrable. The auxiliary condition in the interaction picture is found to have a form analogous to that of the corresponding condition in quantum electrodynamics. In the free-field approximation in which all gravitational self-interactions as well as interactions between the gravitational and other flelds are ignored, it is shown that the auxiliary condition eliminates negative probabilities (which could occur because of the use of Gupta's indefinite metric) and ensures the positive- definiteness of the free-field energy.
- Research Organization:
- Purdue Univ., Lafayette, Ind.
- NSA Number:
- NSA-16-033594
- OSTI ID:
- 4773939
- Journal Information:
- Dissertation Abstr., Journal Name: Dissertation Abstr. Vol. Vol: 23
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
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