Constructive Quantum Field Theory
Jonathan Dimock Principal Investigator
MetadataShow full item record
0070905<br/>Dimock<br/>The goal of this project is to study quantum field theory models<br/>with full mathematical rigor. This is useful to clarify the<br/>structure of quantum field theory, and to enhance its<br/>predictive power. Quantum field theory is primarily a theory<br/>of elementary particle physics, but it also has an important<br/>role to play in classical statistical mechanics. Specific goals<br/>are as follows.<br/>(1.) A construction of quantum electrodynamics<br/>on a three dimensional torus. This is a step toward control<br/>of quantum electrodynamics and/or quantum chromodynamics in<br/>four dimensions, both of central importance in physics.<br/>(2.) The construction of a non-Gaussian fixed point for the<br/>renormalization group for an N-component scalar field in three<br/>dimensions. This would be progress toward understanding a wide<br/>range of critical phenomena.<br/>(3.) A study of the Higgs mechanism for non-Abelian gauge fields<br/>on a lattice. The Higgs mechanism is an important feature of<br/>theories of the weak interactions.