Quantum Spins and Quantum Links: The D-Theory Approach to Field Theory

Abstract

A new non-perturbative approach to quantum field theory is proposed. Instead of performing a path integral over configurations of classical fields, D-theory works with discrete quantized variables. Classical spin fields are replaced by quantum spins, and classical gauge fields are replaced by quantum links. The classical fields of a d-dimensional quantum field theory reappear as low-energy effective degrees of freedom of the discrete variables, provided the (d+1)-dimensional D-theory is massless. When the extent of the extra Euclidean dimension becomes small in units of the correlation length, an ordinary d-dimensional quantum field theory emerges by dimensional reduction. The D-theory formulation of some spin models and gauge theories is constructed explicitly. In particular, QCD emerges as a quantum link model.