Fermionic Geometric Algebra

We are a group that is researching the application of Clifford Algebras to model physics, particularly that Standard Model of particle physics and General Relativity. The goal is to create a single mathematical framework on which both theories can be combined and outstanding problems in physics can be resolved.

Before you venture further, we would highly recommend reading some source material to familiarize yourself with key concepts that we use in Clifford Algebras. This mathematical formalism is extremely simple, but it's worthwhile reading up if you're not familiar and there are a ton of fantastic resources you can check out.

1. Clifford Algebras: An Introduction — D. J. H. Garling
   A solid, textbook-level treatment covering multilinear algebra, quadratic spaces, and real Clifford algebras. Great for advanced undergraduates and researchers.

2. An Introduction to Clifford Algebras and Spinors — Jayme Vaz Jr. & Roldão da Rocha Jr.
   A more advanced text connecting Clifford algebras to spinors and their applications in theoretical physics.

3. Lecture Notes: Clifford Algebra, Geometric Algebra, and Applications (PDF) — Douglas Lundholm & Lars Svensson
   A freely available and very accessible set of notes emphasizing geometry, orthogonal maps, and spinors.

4. Introduction to Geometric (Clifford) Algebra – YouTube
   A clear visual introduction covering the basics: unit-vector products, reduction rules, and the axioms of geometric (Clifford) algebra.

5. Spinors for Beginners 11: What is a Clifford Algebra? – YouTube
   A well-paced bridge between exterior/Grassmann algebra and Clifford algebra, ideal for conceptual clarity.

6. Tutorial on Clifford’s Geometric Algebra – YouTube Playlist — Eckhard Hitzer
   A comprehensive video series covering 2D/3D space, spacetime, blades, and duality for deeper geometric intuition.

As with all scientists, we are bad at telling jokes, so we want to share the punchline first before you spend a lot of time diving into our little rabbit hole. Here are some key ideas and predictions currently made by our theory.

1. TSVF - Two State Vector Formalism
   TSVF leads to the concept of weak values, allowing meaningful measurement results even when traditional (strong) measurement collapses would destroy the system’s state. This has been experimentally confirmed and used in quantum optics and precision metrology.

2. Sterile Neutrinos
   Sterile neutrinos are particles outside the usual Standard Model. They interact only via gravity and are a candidate for Dark Matter.

Please feel free to click around. Discussions will give you a chance to ask us questions and to contribute to the project.