quantum theory of 3+1 gravity and dark matter: a new formulation of the gupta-feynman based quantum field theory of 3+1 einstein gravity

Gravitons and axions play an important role with regard to dark matter.here, by appeal to the developments of gupta and feynman and using a novelmathematical theory based on ultrahyperfunctions, we are able to provide an exact,quantum relativistic expression for the gravitons and axions self-energies. for a completeexplanation of ultrahyperfunctions and their uses in quantum field theory seethe book of plastino and rocca.ultrahyperfunctions (uhf) are in most cases the generalization and extension to thecomplex plane of schwartz tempered distributions. for example, in the book of plastinoand rocca and in the papers of bollini et al. you can find a large number of examplesof ultrahyperfunctions. this manuscript is an application to einstein’s gravity anddark matter (eg) of the mathematical theory developed by bollini et al and continuedfor more than 25 years by one of the authors of this paper. we will quantizeeg using the most general quantization approach, the schwinger-feynman variationalprinciple, which is more appropriate and rigorous than the popular functional integralmethod (fim). fim is not applicable here because our lagrangian contains derivativecouplings. we use the einstein lagrangian as obtained by gupta, but we added a newconstraint to the theory. thus the problem of lack of unitarity for the s matrix thatappears in the procedures of gupta and feynman disappear. furthermore, we considerablysimplify the handling of constraints, eliminating the need to appeal to ghostsfor guaranteeing the unitarity of the theory.our theory is obviously non-renormalizable. however, this inconvenience is solved byresorting to the theory developed by bollini et al. this theory is based on the thesisof alexander grothendieck and on the theory of ultrahyperfunctions. based onthese papers, a complete theory has been constructed for 25 years that is able to quantizenon-renormalizable field theories (ft). because we are using a gupta-feynman based eg lagrangian and to the new mathematical theory we have avoided the use ofghosts, as we have already mentioned, to obtain a unitary qft of eg. moreover theself-energy of the graviton changes its mass and propagator upon interaction with theaxion. the mass of the graviton can increase and the bare propagator changes to thedressed propagator. this phenomenon is measurable, but very difficult to detect sincethe bare mass of the graviton is zero and that of the axion is extremely small. also,for the first time in the literature, we give explicit formulas for the self-energy of thegraviton, interacting and non-interacting with axions. also, for the first time in theliterature, we present 17 graphs corresponding to those self-energies.