Selected Topics in Gravity Field Theory and Quantum Mechanics

<p>Quantum field theory has achieved some extraordinary successes over the past sixty years; however it retains a set of challenging problems. It is not yet able to describe gravity in a mathematically consistent manner. CP violation remains unexplained. Grand unified theories have been eliminated by experiment and a viable unification model has yet to replace them. Even the highly successful quantum chromodynamics despite significant computational achievements struggles to provide theoretical insight into the low-energy regime of quark physics where the nature and structure of hadrons are determined. The only proposal for resolving the fine-tuning problem low-energy supersymmetry has been eliminated by results from the LHC.</p><p>Since mathematics is the true and proper language for quantitative physical models we expect new mathematical constructions to provide insight into physical phenomena and fresh approaches for building physical theories.</p>