Topologically Nontrivial Sectors of Maxwell Field Theory on Riemann Surfaces

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In this paper the Maxwell field theory is considered on a closed and orientable Riemann surface of genus $h>1$. The solutions of the Maxwell equations corresponding to nontrivial values of the first Chern class are explicitly constructed for any metric in terms of the prime form.
8 pages, TeX + harvmac, to appear in Lett. Math. Phys

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