Interaction Picture in Gravitational Theory

Publisher Website
Google Scholar
Abstract
The problem of defining an interaction picture for a quantized version of the Einstein theory of gravitation is considered. The quantization method involves the use of the De Donder condition, as formulated by Fock, as an auxiliary condition on the state vectors. The theory is formulated in a Lorentz-covariant way by assuming the validity of Fock's conjecture that the De Donder-Fock coordinate condition determines the coordinate system up to a Lorentz transformation. It is shown that the interaction operator which appears in the Tomonaga-Schwinger equation obeyed by the interaction-picture state vectors satisfies a necessary integrability condition. Some problems involved in imposing the auxiliary condition on the interaction-picture state vectors are also considered.