Research Projects

General relativity provides consistent classical dynamics of spacetime and matter, while geodesics on spacetime approximate the dynamics of point particles and planets without back reaction. Quantum field theory in curved spacetimes is similar, but may be important in areas like the early stage of the universe or late stages of Hawking radiation when the energy density of matter is order unity. A series of approximations from high energy to low energy is expected: Quantum Gravity — QFT on classical spacetime with back reaction — QFT on classical spacetime. There are ideas about quantum gravity but no clear way to derive the middle link. The oldest idea is semiclassical gravity, where matter stress energy tensor in Einstein field equations is replaced by an expectation value in some quantum state. This has structural issues and requires a proper definition for static or stationary spacetimes. The researchers aim to bridge this gap by studying a novel back reaction model where matter dynamics are dictated by a time-dependent Schrödinger equation, allowing the quantum state of matter and classical gravity variables to evolve self-consistently. This scheme will serve as a toy model sans gravity and investigate models of primordial magneto-genesis in the early Universe. The implementation will be semi-analytical and computational, requiring simultaneous solving coupled partial differential equations and an IVP on a grid simulating real space dynamics.