Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
1997-09-25
Nucl.Phys.Proc.Suppl. 63 (1998) 775-789
Physics
High Energy Physics
High Energy Physics - Lattice
15 pages, LaTeX, including 9 encapsulated postscript figures. Contribution to Lattice 97 by 5 authors, to appear in Nuclear Ph
Scientific paper
10.1016/S0920-5632(97)00900-6
A new non-perturbative approach to quantum field theory --- D-theory --- is proposed, in which continuous classical fields are replaced by discrete quantized variables which undergo dimensional reduction. The 2-d classical O(3) model emerges from the (2+1)-d quantum Heisenberg model formulated in terms of quantum spins. Dimensional reduction is demonstrated explicitly by simulating correlation lengths up to 350,000 lattice spacings using a loop cluster algorithm. In the framework of D-theory, gauge theories are formulated in terms of quantum links --- the gauge analogs of quantum spins. Quantum links are parallel transporter matrices whose elements are non-commuting operators. They can be expressed as bilinears of anticommuting fermion constituents. In quantum link models dimensional reduction to four dimensions occurs, due to the presence of a 5-d Coulomb phase, whose existence is confirmed by detailed simulations using standard lattice gauge theory. Using Shamir's variant of Kaplan's fermion proposal, in quantum link QCD quarks appear as edge states of a 5-d slab. This naturally protects their chiral symmetries without fine-tuning. The first efficient cluster algorithm for a gauge theory with a continuous gauge group is formulated for the U(1) quantum link model. Improved estimators for Wilson loops are constructed, and dimensional reduction to ordinary lattice QED is verified numerically.
Beard Bernard B.
Brower Richard C.
Chandrasekharan Shailesh
Chen Daguang
Tsapalis Antonios
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