@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},
volume = {23},
year = {2006},
pages = {891-909},
doi = {10.1016/j.anihpc.2005.09.006},
mrnumber = {2271700},
zbl = {05138725},
language = {en},
url = {http://dml.mathdoc.fr/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, Tome 23 (2006) pp. 891-909. doi : 10.1016/j.anihpc.2005.09.006. http://gdmltest.u-ga.fr/item/AIHPC_2006__23_6_891_0/
[1] , Sobolev Spaces, Pure Appl. Math., Academic Press, New York, 1975. | MR 450957 | Zbl 0314.46030
[2] , Unitary quantum field theory on the noncommutative Minkowski space, hep-th/0212266v2.
[3] , Analyse fonctionnelle, Masson, 1983. | MR 697382 | Zbl 0511.46001
[4] , On the trees of quantum fields, Eur. Phys. J. C 12 (2000) 535-546, hep-th/9906111.
[5] , Butcher series and renormalization, BIT 19 (2004) 714-741, hep-th/0003202. | MR 2106008
[6] , , Renormalization of QED with planar binary trees, Eur. Phys. J. C 19 (2001) 714-741, hep-th/0003202. | Zbl 1099.81568
[7] , , Random Trees, Lévy Processes and Spatial Branching Processes, Astérisque, vol. 281, 2002. | MR 1954248 | Zbl 1037.60074
[8] , Simplicial properties of the set of planar binary trees, J. Algebraic Combin. (1999). | MR 1817703 | Zbl 0989.17001
[9] , , , 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] , Hamiltonian formalisms for multidimensional calculus of variations and perturbation theory, Contemp. Math. 350 (2004) 127-147. | MR 2082395 | Zbl 1069.58011
[12] , , 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] , , Quantum Field Theory, McGraw-Hill International Book Co., New York, 1980. | MR 585517
[15] , A finite dimensional canonical formalism in the classical field theories, Comm. Math. Phys. 30 (1973) 99-128. | MR 334772
[16] , Spatial Branching Processes, Random Snakes and Partial Differential Equations, Birkhäuser, Boston, 1999. | MR 1714707 | Zbl 0938.60003
[17] , Analyse Fonctionnelle, Ediscience international, 1995.
[18] , , 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] , Some Hopf algebras of trees, math.QA/0106244.