Abstract
The gauging of free differential algebras (FDA's) produces gauge field theories containing antisymmetric tensors. The FDA's extend the Cartan-Maurer equations of ordinary Lie algebras by incorporating p-form potentials (p>1). We study here the algebra of FDA transformations. To every p-form in the FDA, we associate an extended Lie derivative l generating a corresponding ‘gauge’ transformation. The field theory based on the FDA is invariant under these new transformations. This gives geometrical meaning to the antisymmetric tensors. The algebra of Lie derivatives is shown to close and provides the dual formulation of FDA's.
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Sullivan, D.: Infinitesimal computations in topology, Bull. Inst. Hautes Etudes Sci., Publ. Math. 47 (1977).
D'AuriaR. and FréP.: Nuclear. Phys. B 201 (1982) 101; Castellani, L., Fré, P., Giani, F., Pilch, K. and van Nieuwenhuizen, P.: Ann. Phys. 146 (1983), 35; van Nieuwenhuizen, P.: Free graded differential algebras, in: Group Theoretical Methods in Physics, Lecture Notes in Phys. 180, Springer, Berlin, 1983.
CastellaniL., D'AuriaR. and FréP.: Supergravity and Superstrings: a Geometric Perspective, World Scientific, Singapore, 1991.
Ne'emanY. and ReggeT.: Phys. Lett. B 74 (1978) 31; Riv. Nuovo Cimento 1 (1978) 5; D'Adda, A., D'Auria, R., Fré, P. and Regge, T.: Riv. Nuovo Cimento 3 (1980), 6; D'Auria, R., Fré, P. and Regge, T.: Riv. Nuovo Cimento 3 (1980) 12.
CastellaniL., Internat. J. Modern. Phys. A 7 (1992), 1583.
BoukraaS.: Nuclear. Phys. B 303 (1988), 237.
ChevalleyC. and EilenbergS.: Trans. Amer. Math. Soc. 63 (1948), 85.
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Castellani, L., Perotto, A. Free differential algebras: Their use in field theory and dual formulation. Lett Math Phys 38, 321–330 (1996). https://doi.org/10.1007/BF00398356
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DOI: https://doi.org/10.1007/BF00398356