D-Theory: Field Quantization by Dimensional Reduction of Discrete Variables

TL;DR

D-theory offers a non-perturbative framework for quantum field theories using discrete variables like quantum spins and links, which reduce to classical fields in low-energy limits via dimensional reduction.

Contribution

It introduces a novel formulation of quantum field theories through discrete variables and demonstrates how classical fields emerge from this framework in the massless limit.

Findings

Constructed D-theory formulations for scalar and gauge fields.

Showed how classical fields arise as low-energy effective degrees of freedom.

Analyzed the dimensional reduction mechanism in D-theory.

Abstract

D-theory is an alternative non-perturbative approach to quantum field theory formulated in terms of discrete quantized variables instead of classical fields. Classical scalar fields are replaced by generalized 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 scalar field theories with various global symmetries and of gauge theories with various gauge groups is constructed explicitly and the mechanism of dimensional reduction is investigated.