The physics of ``particles of spin ≤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∞-algebra), we have now reproduced their structure entirely
algebraically, hopefully shedding some light on what is going on.Comment: 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 reference