Noether's variational theorem II and the BV formalism

We review the basics of the Lagrangian approach to field theory and recast Noether's Second Theorem formulated in her language of dependencies using a slight modernization of terminology and notation. We then present the Cattaneo-Felder sigma model and work out the Noether identities or dependencies for this model. We review the description of the Batalin-Vilkovisky formalism and show explicitly how the anti-ghosts encode the Noether identities in this example.Comment: 15 pages, submitted to the Proceedings of the 2002 Winter School ``Geometry and Physics'', Srni, Czech Republi

Sh-Lie algebras Induced by Gauge Transformations

The physics of ``particles of spin $\leq 2$'' leads to representations of a Lie algebra $\Xi$ of gauge parameters on a vector space $\Phi$ 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.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

Emil Minchev

msp 2014 vol. 7, no. 5 involv