M-Theory, the Witten Equation and Picard-Lefschetz Theory

'Edward Witten is often likened to Einstein; one colleague reached even further back for a comparison, suggesting that Witten possessed the greatest mathematical mind since Newton' ~ John Horgan

This is a series of posts that hopefully will culminate in a book I am working on. The aim is to show that the Witten equation in the context of Picard-Lefschetz Theory, leads to the non-forking, super-stability and hyper-categoricity of M-theory, thus making it the 'only-game-in-town' indeed. First, I will analyse the Witten nonlinear elliptic system of PDEs associated with a quasi-homogeneous polynomial-super-potential by showing its depth via the Landau-Ginzburg/Calabi-Yau correspondence.

The Dirac-Born-Infeld Action, D-Branes and Spacetime Symmetries

Ex nihilo nihil fit ~ Parmenides

In this post, in order to solve the Wheeler-deWitt problem-of-time discussed by me, and since string/M-theoretic braneworld cosmology offers the only solution in a unified C*-Heisenberg-algebraic sense, I must first analyse a field theory on a D-brane sigma worldvolume and study the Dirac-Born-Infeld action

The Wheeler-DeWitt Metric, Indefiniteness, Quantum Cosmology, and Gravity

Go down deep enough into anything and you will find mathematics ~ Dean Schlicter

The unification problem in physics has at its heart the problem of time: quantum physics, via the Heisenberg Uncertainty Principle between time and energy is not compatible with the Einstein notion of time as coupled with space that gives rise to a 'smooth' spacetime continuum. John Wheeler and Bryce DeWitt did successfully resolve this incompatibility via the Wheeler-DeWitt equation: however, at two high prices. One, time ceases to play any dynamical role in the universe since it occurs idly in the equation, and secondly, by metaplectic geometry, there can be no quantum cosmological universal metric definable. In this post, I will try and analyse the metric problem and leave my analysis of the Page-Wootters 'solution' to the WdW problem of time for another post.