\(\mathbb{Z}_2\)-graded cocycles in higher dimensions (Q1392681)

Current superalgebras and corresponding Schwinger terms in 1 and 3 space dimensions are studied. This is done by generalizing the quantization of chiral fermions in an external Yang-Mills potential to the case of a \(\mathbb{Z}_2\)-graded potential coupled to bosons and fermions. This is a supersymmetric generalization of the cocycles of \textit{L.-E. Lundberg} [Commun. Math. Phys. 50, 103-112 (1976; Zbl 0336.46062)] and \textit{J. Mickelsson} [ibid. 97, 361-370 (1985; Zbl 0781.22016)].