Nicolai maps and fermion sectors

• Published in: Annals of physics Vol. 166; no. 1; pp. 33 - 75
• Main Authors: Claudson, M, Halpern, M.B
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 1986; Elsevier
• Subjects: Classical and quantum physics: mechanics and fields; Exact sciences and technology; Physics; Theory of quantized fields; Supersymmetry; Quantum field theory; Gauge theory
• ISSN: 0003-4916; 1096-035X
• DOI: 10.1016/0003-4916(86)90051-5

Nicolai maps, and particularly their fermion sector structure, are explored over a broad variety of supersymmetric theories. Studies are made in the Witten model, the N = 2 supersymmetric sigma model in 1 + 0 dimensions, dimensionally reduced Wess-Zumino models, and N = 1 Yang-Mills in D = 4. In general each theory yields families of Nicolai maps, each map being a Langevin equation, equivalent to the dynamics of a particular sector. We also detail the remarkable fact that closed form Nicolai maps exist for a few ordinary bosonic nonsupersymmetric theories, with ordinary QCD 4 as an important example. These bosonic theories correspond to “null-fermion” sectors of supersymmetric theories, in which the fermions fail to contribute.