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Sh-Lie algebras Induced by Gauge Transformations

Ron Fulp·Tom Lada·Jim Stasheff
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Abstract

The physics of ``particles of spin $\leq 2$'' leads to representations of a Lie algebra $Ξ$ of gauge parameters on a vector space $Φ$ of fields. Attempts to develop an analogous theory for spin $>2$ 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 ($L_\infty$-algebra), we have now reproduced their structure entirely algebraically, hopefully shedding some light on what is going on.

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BibTeXRIS

Ron Fulp, Tom Lada, Jim Stasheff. 2001-12-15. Sh-Lie algebras Induced by Gauge Transformations. https://arxiv.org/abs/math/0012106

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