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You cannot distinguish this, they are all symmetric. The hopping that is clockwise with respect to one cell is anticlockwise with respect to the neighboring cell. If you add this "with respect to", then orientation is meaningfull. Well, any graph can be oriented. Just arbitrarily chose for each edge a positive direction and call the other one negative. ...


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Yes, any group can be a gauge group. To each oriented edge of the lattice you assign a group element, with the opposite orientations of an edge associated to inverse group elements. The observables are conjugacy classes of products of group elements around a loop of oriented edges. The most basic such observable is the product of group elements around an ...



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