New Science Series
We study the O(N) generalization of the σ model in the limit of large N, for four, three, two, and one space-time dimensions. We compute the effective potential and some momentum-dependent Green's functions. In one and two dimensions, spontaneous symmetry breakdown is impossible; any asymmetric minimum inserted in the tree-approximation potential is immediately filled in by the effects of radiative corrections. This is in agreement with general theorems. In four dimensions, the model is inconsistent; it possesses a tachyon. In three dimensions, the model seems to be consistent, and offers an interesting example of some nonlinear effects associated with spontaneous symmetry breakdown that are not present in the usual (tree-approximation) models.
BREAKING NEWS... 2 DEC 2008 ~R~equiem for a Word: |Q/works: The Unholly Continuam
avoid this problem by using geometric phase shifts in the design of quantum gates to perform information processing. Experiments and simulations have shown that these gates may be tolerant to certain types of faults, and may therefore be useful for robust quantum computation.
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