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

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

2003-09-29

arxiv.org/abs/hep-lat/0309182v1

Nucl.Phys. B693 (2004) 149-175

Physics

High Energy Physics

High Energy Physics - Lattice

30 pages, no figures

Scientific paper

10.1016/j.nuclphysb.2004.06.007

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.

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