Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2000-12-11
Phys.Rev. D63 (2001) 085007
Physics
High Energy Physics
High Energy Physics - Lattice
Scientific paper
10.1103/PhysRevD.63.085007
Quantum spin and quantum link models provide an unconventional regularization of field theory in which classical fields arise via dimensional reduction of discrete variables. This D-theory regularization leads to the same continuum theories as the conventional approach. We show this by deriving the low-energy effective Lagrangians of D-theory models using coherent state path integral techniques. We illustrate our method for the $(2+1)$-d Heisenberg quantum spin model which is the D-theory regularization of the 2-d O(3) model. Similarly, we prove that in the continuum limit a $(2+1)$-d quantum spin model with $SU(N)_L\times SU(N)_R\times U(1)_{L=R}$ symmetry is equivalent to the 2-d principal chiral model. Finally, we show that $(4+1)$-d SU(N) quantum link models reduce to ordinary 4-d Yang-Mills theory.
Schlittgen B.
Wiese Uwe-Jens
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