The Plebanski action

Jerzy Plebanski was a great man. He was born in Poland and died in Mexico City. Unfortunately we did not interact as much as I would have liked. He was the first director of the Physics Department where I got my Master's Degree at Centro de Investigacion y Estudios Avanzados (CINVESTAV), Instituto Politecnico Nacional (IPN), in Mexico City. By the time I got to CINVESTAV he was back in Poland, then I went to California, and he came to stay in Mexico.

Prof. Plebanski worked with Leopold Infeld, another great Polish physicist that wrote the "Evolution of Physics" with Albert Einstein, a classic science popularization book. Here I want to pay tribute to this great physicist. He discovered how to separate einsteinean substructures in General Relativity in 1976. This was unknowingly used by Ashtekar to prove that General Relatvity (GR) is a Gauge Theory.

"All known classical gravity theories such as GR and supergravity in any dimension are diffeomorphism invariant gauge theories. Hence they all provides examples of causal spin network theories. But it's even better than this, because the dynamics turns out to act simply on the spin network states, through local moves of the kind described above. This is a consequence of the second principle, which is that the dynamics of all known classical relativistic gravitational theories are arrived by perturbing around[14] or constraining topological field theories[15]. In 4 dimensions one route to this is through the Plebanski action[16]."

This quote is from a recent review by Lee Smolin of Quantum Gravity theories.

http://lanl.arxiv.org/abs/hep-th/0605052

This is relevant science because my generation of physicists is trying to construct a Quantum Theory of Gravity, and Plebanski's decomposition of Einstein's Theory is considered an important step in unifying the mathematical structures of quantum theory and classical Differential Geometry, which is the foundation of General Relativity.

The Plebanski action is a simple code to express the dynamics of space time.