Planar binary trees and perturbative calculus of observables in classical field theory
Annales de l'I.H.P. Analyse non linéaire, Volume 23 (2006) no. 6, p. 891-909
@article{AIHPC_2006__23_6_891_0,
     author = {Harrivel, Dikanaina},
     title = {Planar binary trees and perturbative calculus of observables in classical field theory},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {23},
     number = {6},
     year = {2006},
     pages = {891-909},
     doi = {10.1016/j.anihpc.2005.09.006},
     zbl = {05138725},
     mrnumber = {2271700},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2006__23_6_891_0}
}
Harrivel, Dikanaina. Planar binary trees and perturbative calculus of observables in classical field theory. Annales de l'I.H.P. Analyse non linéaire, Volume 23 (2006) no. 6, pp. 891-909. doi : 10.1016/j.anihpc.2005.09.006. http://www.numdam.org/item/AIHPC_2006__23_6_891_0/

[1] Adams R.A., Sobolev Spaces, Pure Appl. Math., Academic Press, New York, 1975. | MR 450957 | Zbl 0314.46030

[2] Bahns D., Unitary quantum field theory on the noncommutative Minkowski space, hep-th/0212266v2.

[3] Brezis H., Analyse fonctionnelle, Masson, 1983. | MR 697382 | Zbl 0511.46001

[4] Brouder C., On the trees of quantum fields, Eur. Phys. J. C 12 (2000) 535-546, hep-th/9906111.

[5] Brouder C., Butcher series and renormalization, BIT 19 (2004) 714-741, hep-th/0003202. | MR 2106008

[6] Brouder C., Frabetti A., Renormalization of QED with planar binary trees, Eur. Phys. J. C 19 (2001) 714-741, hep-th/0003202. | Zbl 1099.81568

[7] Duquesne T., Le Gall J.-F., Random Trees, Lévy Processes and Spatial Branching Processes, Astérisque, vol. 281, 2002. | MR 1954248 | Zbl 1037.60074

[8] Frabetti A., Simplicial properties of the set of planar binary trees, J. Algebraic Combin. (1999). | MR 1817703 | Zbl 0989.17001

[9] Graham R., Knuth D., Patashnik O., Concrete Mathematics. A Foundation for Computer Science, Addison-Wesley, New York, 1989. | MR 1397498 | Zbl 0668.00003

[10] D. Harrivel, Non linear control and perturbative expansion using Planar Trees, 2005, in press.

[11] Hélein F., Hamiltonian formalisms for multidimensional calculus of variations and perturbation theory, Contemp. Math. 350 (2004) 127-147. | MR 2082395 | Zbl 1069.58011

[12] Hélein F., Kouneiher J., Finite dimensional Hamiltonian formalism for gauge and quantum field theory, J. Math. Phys. 43 (2002) 5. | MR 1893674 | Zbl 1059.70019

[13] F. Hélein, J. Kouneiher, Lepage-Dedecker general multisymplectic formalisms, Adv. Theor. Math. Phys. (2004), in press.

[14] Itzykson C., Zuber J.-B., Quantum Field Theory, McGraw-Hill International Book Co., New York, 1980. | MR 585517

[15] Kijowski J., A finite dimensional canonical formalism in the classical field theories, Comm. Math. Phys. 30 (1973) 99-128. | MR 334772

[16] Le Gall J.-F., Spatial Branching Processes, Random Snakes and Partial Differential Equations, Birkhäuser, Boston, 1999. | MR 1714707 | Zbl 0938.60003

[17] Rudin W., Analyse Fonctionnelle, Ediscience international, 1995.

[18] Sedgewick R., Flajolet P., An Introduction to the Analysis of Algorithms, Addison Wesley Professional, New York, 1995. | Zbl 0841.68059

[19] W.M. Tulczyjew, Geometry of phase space. Seminar in Warsaw, 1968.

[20] Van Der Lann P., Some Hopf algebras of trees, math.QA/0106244.