Lie and Leibniz Algebras of LowerDegree Conservation Laws
Abstract
A relationship between the asymptotic and lowerdegree 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 lowerdegree conservation laws vanish modulo central charges, the corresponding Leibniz algebra degenerates into a Lie one. The general construction is illustrated by two standard examples: YangMills theory and Einstein's gravity.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 arXiv:
 arXiv:2107.11261
 Bibcode:
 2021arXiv210711261E
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics;
 70S10;
 81T70;
 83C40
 EPrint:
 28 pages