Lie and Leibniz Algebras of Lower-Degree Conservation Laws
arXiv:2107.11261 · doi:10.1088/1751-8121/ac477d
Abstract
A relationship between the asymptotic and lower-degree conservation laws in (non-)linear gauge theories is considered. We show that the true algebraic structure underlying asymptotic charges is that of Leibniz rather than Lie. The Leibniz product is defined through the derived bracket construction for the natural Poisson brackets and the BRST differential. Only in particular, though not rare, cases that the Poisson brackets of lower-degree conservation laws vanish modulo central charges, the corresponding Leibniz algebra degenerates into a Lie one. The general construction is illustrated by two standard examples: Yang-Mills theory and Einstein's gravity.
arXiv comment28 pages; v2: minor corrections, a reference added; v3 typos corrected
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