sh-Lie Algebras Induced by Gauge Transformations

Traditionally symmetries of field theories are encoded via Lie group actions, or more generally, as Lie algebra actions. A significant generalization is required when “gauge parameters” act in a field dependent way. Such symmetries appear in several field theories, most notably in a “Poisson induced” class due to Schaller and Strobl SS94] and to Ikeda Ike94], and employed by Cattaneo and Felder CF99] to implement Kontsevich's deformation quantization Kon97]. Consideration of “particles of spin > 2” led Berends, Burgers and van Dam Bur85,BBvD84,BBvD85] to study “field dependent parameters” in a setting permitting an analysis in terms of smooth functions. Having recognized the resulting structure as that of an sh-Lie algebra (L _∞-algebra), we have now formulated such structures entirely algebraically and applied it to a more general class of theories with field dependent symmetries. Received: 14 December 2000 / Accepted: 8 February 2002?Published online: 2 October 2002