Resumen
Revisamos como construir el operador de Paneitz en cuatro dimensiones y el correspondiente operador en seis dimensiones, mediante la construcción de funcionales diferenciales bilineales simétricos que son conformemente invariantes.
Citas
Branson, T.P. (2001) “Automated symbolic computations in spin geometry”, in: F. Brackx, J.S.R. Chisholm & V. Souček (Eds.) Clifford Analysis and its Applications, NATO Science Series II, Vol. 25, Kluwer Academic Publishers, Dordrecht: 27–38.
Branson, T.P. (1985) “Differential operators canonically associated to a conformal structure”, Math. Scand. 57: 293–345.
Connes, A. (1995) “Quantized calculus and applications”, in: Proceedings of the XIth International Congress of Mathematical Physics, International Press, Cambridge, MA: 15–36.
Fefferman, C.; Graham, C.R. (1985) Conformal Invariants. In Élie Cartan et les mathématiques d’aujourd’hui , Astérisque, hors série, Société Mathé- matique de France: 95–116.
Graham, R.; Jenne, R.; Mason, L.; Sparling, G. (1992) “Conformally invariant powers of the Laplacian, I: Existence”, J. London Math. Soc. (2) 46: 557–565.
Gover, A. R.; Peterson, L.J. (2003) “Conformally invariant powers of the Laplacian, Q-curvature and tractor calculus”, Comm. Math. Phys. 235(2): 339–378.
Lee, J.M. (s.f.) “A Mathematica package for doing tensor calculations in differential geometry”, available at http://www.math.washington.edu/∼lee/Ricci/.
Paneitz, S. (1983) “A quartic conformally covariant differential operator for arbitrary pseudo-Riemannian manifolds”, preprint, Massachusetts Institute of Technology.
Phillips, N.G.; Hu, B.L. (2003) “Noise kernel and stress energy bi-tensor of quantum fields in conformally-optical metrics: Schwarzschild black holes”, Phys. Rev. D (3) 67(10) 104002, 26 pp.
Phillips, N.G.; Hu, B.L. (2001) “Noise kernel and stress energy bi-tensor of quantum fields in hot flat space and Gaussian approximation in the optical Schwarzschild metric”, Phys. Rev. D (3) 63(10) 104001, 16 pp.
Tsantalis, E.; Puntigam, R.A.; Hehl, F.W. (1996) “A quadratic curvature Lagrangian of Pawlowski and Raczka: a finger exercise with math tensor”, Relativity and Scientific Computing, Springer, Berlin: 231–240.
Ugalde, W.J. (2006) “A construction of critical GJMS operators using Wodzicki’s residue” Comm. Math. Phys. 261(3): 771–788.