Abstract
By considering the geometry of the central extension of the loop group as a principal bundle it is shown that it must be the quotient of a larger group. This group is a central extension of the group of paths in the loop group and its cocycle is constructed as the holonomy around a certain path. Conversely it is shown that this definition of a cocycle gives a method of constructing the central extension. The Wess-Zumino term plays an important role in these constructions.
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Communicated by A. Jaffe
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Murray, M.K. Another construction of the central extension of the loop group. Commun.Math. Phys. 116, 73–80 (1988). https://doi.org/10.1007/BF01239026
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DOI: https://doi.org/10.1007/BF01239026