# George Sowers' Dissertation & *A Prolegomena for a Quantum Reformation*

*Monte Carlo Algorithms for Fully Interacting Lattice Gauge Theory*

George completed his Ph.D. dissertation, *Monte Carlo Algorithms for Fully Interacting Lattice Gauge Theory*, in 1988. Lattice gauge theory is a method for simulating quark theory on a computer. It is analogous to computational fluid dynamics (CFD) in that it takes a theory formulated in a continuum and puts it on a lattice or discrete grid. The intractable partial differential equations of the continuum then become a system of equations that can be solved by computational means.

George developed unique algorithms for including the fermion fields. Because of the Pauli exclusion principle, two fermions can never occupy the same state. In the abstract field theory formulation, fermions are represented by Grassman variables, which means they anti-commute (i.e., AB=-BA). To make a long story short, one of the computational problems in doing these simulations involved counting the number of unique paths between two points on the lattice. For fermions, paths that stepped backward at any point gave a zero contribution because of the anti-commuting property. George did some fun number theoretic work to come up with a formula to count exactly the number of paths between any two points without backstepping.

He then applied these algorithms to some toy models to prove their effectiveness. George had been wrestling with the counting problem for some time. The critical insight came while driving across the Nevada desert on his way to climb in Yosemite Valley. The method that popped into his head was entirely different from what he had been working on. George immediately pulled over to write it down.