Abstract:
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.
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Received: 14 December 2000 / Accepted: 8 February 2002¶Published online: 2 October 2002
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Fulp, R., Lada, T. & Stasheff, J. sh-Lie Algebras Induced by Gauge Transformations. Commun. Math. Phys. 231, 25–43 (2002). https://doi.org/10.1007/s00220-002-0678-3
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DOI: https://doi.org/10.1007/s00220-002-0678-3