Principia Physicae Generalis

After reviewing some basic ideas in algebraic topology, we look at what a topological index is and how it can help us find new physics.

We look at some simple systems in quantum mechanics that can be interpreted gemoetricaly through some basic concepts of topology.

We derive the basic equations of quantum mechanics and field theory using only symmetry and redundancy. We elucidate the concept of gauge symmety.

We explore the star-triangle relation in statistical mechanics and see how, through knot theory it can connect to a multitude of other, exactly solvable systems in physics

After demonstrating the connection between black holes and entropy we see how gravity can be possibly interpreted as an entropic force

After explaining the philosophy behind the Renormalisation Group, we apply it to derive the Navier-Stokes equations and explain their universality.

An arithmetic method for finding the spectrum of QM systems based on the demand for unitarity

We look at the geometries that arise from the equations of special relativity, classical mechanics and quantum mechanics. We then extract some interesting properties of each theory by considering the “rotations” in each geometry.

A summary of constraints in the Hamiltonian formalism and their connection to gauge symmetry. The classical field theory of Electrodynamics is quantized using constraints.

An explanation of constraints in classical mechanics and the derivation of the Navier-Stokes equations, treating pressure as a Lagrange multiplier.