Shows that nilpotent commuting scalar fields exhibit behavior similar to random walks, suggesting new connections in field theory.
We show that the correlation functions of a free nilpotent commuting scalar field are equal to the correlation functions of a random walk where paths with odd number of crossings give a negative contribution. It follows that in a number of dimensions where the self-avoidind random walk is a free theory in the continuum limit, the nilpotent commuting scalar behaves as an ordinary scalar. We show how a nilpotent commuting scalar can be to an abelian gauge field.
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Palumbo F. (1993) studied this question.
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