An equation of motion for the theory of computation
Mentor:Matilde Marcolli, Professor of Mathematics, California Institute of Technology
A new connection has recently been made between two seemingly unrelated subjects – physics and theoretical computer science. In quantum field theory, the mathematical language of particle physics, particle interactions can be thought of as built up out of sub-interactions. It was realized that this bears a mathematical similarity to the way computer programs are built out of smaller programs in the theory of computation, the mathematical abstraction of computers. The common mathematical framework underlying both subjects can be used to draw further connections between quantum field theory and the theory of computation. We have investigated the equations of motion, which in physics characterize the behavior of a system of particles, in the context of the theory of computation. These equations, called Dyson-Schwinger equations, give new meaning to problems in computation. By studying the mathematical connections between physics and computer science, we can approach both subjects with a fresh perspective as well as make new developments in related subjects such as quantum computation.