Sh-Lie algebras Induced by Gauge Transformations
Abstract
The physics of ``particles of spin '' leads to representations of a Lie algebra of gauge parameters on a vector space of fields. Attempts to develop an analogous theory for spin have failed; in fact, there are claims that such a theory is impossible (though we have been unable to determine the hypotheses for such a `no-go' theorem). This led BBvD [burgers:diss,BBvd:three,BBvD:probs] to generalize to `field dependent parameters' in a setting where some analysis in terms of smooth functions is possible. Having recognized the resulting structure as that of an sh-lie algebra (-algebra), we have now reproduced their structure entirely algebraically, hopefully shedding some light on what is going on.
Cite
@article{arxiv.math/0012106,
title = {Sh-Lie algebras Induced by Gauge Transformations},
author = {Ron Fulp and Tom Lada and Jim Stasheff},
journal= {arXiv preprint arXiv:math/0012106},
year = {2007}
}
Comments
Now 24 pages, LaTeX, no figures Extensively revised in terms of the applications and on shell aspects. In particular, a new section 8 analyzes Ikeda's 2D example from our perspective. His bracket is revealed as a generalized Kirillov-Kostant bracket. Additional references