Some New Aspects of Quantum Gravity Involving Coupling of Fields to Random Currents with Applications to Astroparticle Physics

Some basic questions in quantum field theory and cosmology are addressed here. We derive some formulas for the change in the canonical commutation and anticommutation relations at equal time for some of the well known quantum fields in the presence of a background curved space-time metric. We study the problem of quantizing the Klein-Gordon field interacting with the gravitational field of homogeneous and isotropic space time of an expanding universe and also simultaneously interacting with a classical random current field. Formulas for the quantum effective action of the scale factor of the expanding universe are derived by averaging over the Klein-Gordon field, taking into account its interaction with a classical random current field. This gives us information about how the expansion rate of our universe can get affected due to quantum mechanical interaction effects. Finally, we discuss the general problem of symmetry breaking in the quantum effective action of a field when it interacts with a random Gaussian current field source. The symmetry breaking terms are expressed in terms of the correlation field of the random current source. Since the Hessian of the quantum effective action equals the inverse of the propagator kernel, it follows that the former tells us how much mass do particles gain by interacting with a random current field. This fact could provide us with a clue about how particles in our universe acquire masses. We then derive Hawking’s temperature formula for a quantum Blackhole using the approximate solution to the Klein-Gordon equation in the vicinity of the Schwarzchild radius. This is a new derivation not present in the literature. Finally, a short discussion is presented about the quantum mechanical meaning of estimating the state of a gravitational wave from continuous noisy measurements on the electromagnetic field with which it interacts on a real time basis using the well known Belavkin quantum filter based on the Hudson-Parthasarathy noisy Schrodinger equation. The appendix provides a simplified analysis of loop quantum gravity based on Ashtekar’s variables and how one constructs the area operator that is crucial in deriving the blackhole entropy.