Abstract
The Vinogradov C-spectral sequence for the Yang–Mills equations is considered and the ‘three-line’ theorem for the term E1 of the C-spectral sequence is proved: E1 p,q = 0 if p > 0 and q < n − 2, where n is the dimension of spacetime.
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Anderson, I. M.: Introduction to the variational bicomplex, in: Mathematical Aspects of Classical Field Theory, Contemp. Math. 132, Amer. Math. Soc., Providence, R.I., 1992, pp. 51-73.
Barnich, G., Brandt, F., and Henneaux, M.: Local BRST cohomology in the antifield formalism: I. General theorems, Comm. Math. Phys. 174 (1995), 57-92, hep-th/9405109.
Bryant, R. L. and Griffiths, P. A.: Characteristic cohomology of differential systems (I): General theory, J. Amer. Math. Soc. 8 (1995), 507-596.
Gessler, D.: On the Vinogradov \({\mathcal{C}}\)-spectral sequence for determined systems of differential equations, Differential Geom. Appl. 7 (1997), 303-324.
Verbovetsky, A.: Notes on the horizontal cohomology, in: M. Henneaux, J. Krasil'shchik, and A. Vinogradov (eds), Secondary Calculus and Cohomological Physics, Contemp. Math. 219, Amer. Math. Soc., Providence, R.I., 1998, pp. 211-231.
Henneaux, M. and Teitelboim, C.: Quantization of Gauge Systems, Princeton University Press, 1992.
Khorkova, N. G.: On the \({\mathcal{C}}\)-spectral sequence of differential equations, Differential Geom. Appl. 3 (1993), 219-243.
Krasil'shchik, I. S., Lychagin, V. V., and Vinogradov, A. M.: Geometry of Jet Spaces and Nonlinear Differential Equations, Gordon and Breach, New York, 1986.
Marvan, M.: On the \({\mathcal{C}}\)-spectral sequence with ‘general’ coefficients, in: Differential Geometry and Its Applications, Proc. Conf., 27 Aug.–2 Sept. 1989, Brno, Czechoslovakia, World Scientific, Singapore, 1990, pp. 361-371.
Tsujishita, T.: Homological method of computing invariants of systems of differential equations, Differential Geom. Appl. 1 (1991), 3-34.
Vinogradov, A. M.: A spectral sequence associated with a nonlinear differential equation, and algebro-geometric foundations of Lagrangian field theory with constraints, Soviet Math. Dokl. 19(1) (1978), 144-148.
Vinogradov, A. M.: Geometry of nonlinear differential equations, Itogi nauki i tekniki, Problemy geometrii 11 (1980), 89-134 (Russian); English transl. in J. Soviet Math. 17 (1981), 1624–1649.
Vinogradov, A. M.: The \({\mathcal{C}}\)-spectral sequence, Lagrangian formalism and conservation laws, J. Math. Anal. Appl. 100 (1984), 1-129.
Vinogradov, A. M. (ed.): Symmetries of Partial Differential Equations: Conservation Laws, Applications, Algorithms, Kluwer Acad. Publ., Dordrecht, 1989.
Vinogradov, A. M.: From symmetries of partial differential equations towards secondary ('quantized') calculus, J. Geom. Phys. 14 (1994), 146-194.
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Gessler, D. The ‘Three-Line’ Theorem for the Vinogradov C-Spectral Sequence of the Yang–Mills Equations. Acta Applicandae Mathematicae 56, 139–153 (1999). https://doi.org/10.1023/A:1006165531180
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DOI: https://doi.org/10.1023/A:1006165531180