Recent work of Hohm and Zwiebach has called attention to the relevance and perhaps prevalence of L∞-structures in field theories in physics. Such structures first achieved physical prominence in Zwiebach’s closed string field theory (CSFT) but hark back to earlier work of Berends, Burgers and van Dam . Essential to both these approaches to field theory is the possibility of field dependence of the gauge algebra and the corresponding gauge transforamtions/symmetries.
Hohm and Zwiebach introduce what they call a standard-form field theory which assumes an L∞-structure; they then show existence in some known gauge field theories, e.g. Yang-Mills. In contrast, Berends, Burgers and van Dam search for a new field theory for higher spin particles. Their assumption of field dependence was shown by Fulp, Lada and Stasheff to lead to an L∞- structure, though less extensive that of Hohm and Zwiebach ..
Our purpose is to extend the Berends, Burgers and van Dam hypothesis to include ‘equations of motion’ and delineate the correspondence with standard- form field theory. We then investigate a deformation theory analysis of the search for a field theory for higher spin particles.