Quantum spins and quantum links: The D-theory approach to field theory

A new non-perturbative approach to quantum field theory is proposed. Instea d of performing a path integral over configurations of classical fields, D- theory works with discrete quantized variables. Classical spin fields are r eplaced by quantum spins, and classical gauge fields are replaced by quantu m links. The classical fields of a d-dimensional quantum field theory reapp ear as low-energy effective degrees of freedom of the discrete variables, p rovided 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 redu ction. The D-theory formulation of some spin models and gauge theories is c onstructed explicitly. In particular, QCD emerges as a quantum link model.