Nonassociativity, Dirac monopoles and Aharonov-Bohm effect

The Aharonov-Bohm (AB) effect for the singular string associated with the Dirac monopole carrying an arbitrary magnetic charge is studied. It is shown that the emerging difficulties in explanation of the AB effect may be removed by introducing nonassociative path-dependent wave functions. This provides the absence of the AB effect for the Dirac string of magnetic monopole with an arbitrary magnetic charge.Comment: Revised version. Typos corrected. References adde

Resonance varieties and Dwyer-Fried invariants

The Dwyer-Fried invariants of a finite cell complex X are the subsets \Omega^i_r(X) of the Grassmannian of r-planes in H^1(X,\Q) which parametrize the regular \Z^r-covers of X having finite Betti numbers up to degree i. In previous work, we showed that each \Omega-invariant is contained in the complement of a union of Schubert varieties associated to a certain subspace arrangement in H^1(X,\Q). Here, we identify a class of spaces for which this inclusion holds as equality. For such "straight" spaces X, all the data required to compute the \Omega-invariants can be extracted from the resonance varieties associated to the cohomology ring H^*(X,\Q). In general, though, translated components in the characteristic varieties affect the answer.Comment: 39 pages; to appear in "Arrangements of Hyperplanes - Sapporo 2009," Advanced Studies in Pure Mathematic