Quantum mechanics of the interaction of gravity with electrons: theory of a spin-two field coupled to energy
Abstract
Two methods of finding the energy tensor from the Lagrangian
of a system are those of Belinfante, and Landau and Lifschitz. Neither of these methods are unique; two energy tensors for the same system differ by a term that is symmetric, has zero divergence, and is itself
a second derivative. It is shown that such a term in the energy tensor produces physical effects that in one case can be measured experimentally. It is because of this lack of uniqueness of energy tensors that it is not sufficient to consider gravity merely as a spin-two field coupled
to energy.
To set up the quantum mechanics of gravity interacting with
electrons, the curved space Lagrangian for the Dirac field is expanded in terms of the gravitational fields h_(µν) is checked that the expanded Lagrangian has the same transformation properties as the original curved space Lagrangian.
The calculations presented are the gravitational Rutherford
scattering of electrons, emission of low energy gravitons by electrons, the scattering of gravitons by electrons, the gravitational self-energy of the electron, and the most divergent part of the vacuum polarization
calculation. There is also an investigation of the effects of the spin of the electron by comparison with a spin-zero particle interacting with gravity.
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