T. S. Kuo and E. Osnes, Folded-Diagram Theory of the Effective Interaction in Nuclei, Atoms and Molecules, Lecture Notes in Physics, vol.364, 1990.

. Morita, Perturbation Theory for Degenerate Problems of Many-Fermion Systems, Progress of Theoretical Physics, vol.29, issue.3, pp.351-69, 1963.
DOI : 10.1143/PTP.29.351

. Jolicard, A recursive solution to the time dependent Schr??dinger equation using a generalized quasidegenerate Bloch formalism, The Journal of Chemical Physics, vol.90, issue.4, pp.2320-2327, 1989.
DOI : 10.1063/1.455973

J. P. Jolicard and . Killingbeck, The Bloch wave operator: generalizations and applications: II. The time-dependent case, Journal of Physics A: Mathematical and General, vol.36, issue.40, pp.411-473, 2003.
DOI : 10.1088/0305-4470/36/40/R01

. Pauli, Selected Topics in Field Quantization, 1973.

. Lindgren, The Rayleigh-Schrodinger perturbation and the linked-diagram theorem for a multi-configurational model space, Journal of Physics B: Atomic and Molecular Physics, vol.7, issue.18, pp.2441-70, 1974.
DOI : 10.1088/0022-3700/7/18/010

. Kvasni?ka, Construction of model hamiltonians in framework of Rayleigh-Schr??dinger perturbation theory, Czechoslovak Journal of Physics, vol.13, issue.6, pp.605-620, 1974.
DOI : 10.1007/BF01587295

J. Gurau, V. Magnen, and . Rivasseau, Tree Quantum Field Theory, Annales Henri Poincar??, vol.72, issue.1, pp.867-91, 2009.
DOI : 10.1007/s00023-009-0002-2
URL : https://hal.archives-ouvertes.fr/hal-00315659

D. Maassen, . Botvich, . Galton-watson-estimate-for-dyson-series, . Ann, and . Poincaré, 10 When H0 is quadratic, the time-dependence of the annihilation operators is simply ane ???nt , where ?n is the energy of the nth eigenvalue of H0 (see, e.g. ref. 42). When H0 is not quadratic, the time-dependent annihilation operators and the free Feynman propagator cannot be calculated explicitly, pp.1141-58, 2009.

N. Bulaevskii, Quasihomopolar electron levels in crystals and molecules, J. Exp. Theor. Phys, vol.24, pp.154-60, 1967.

E. Delsole and . Fiorino, Macroscopic dielectric tensor at crystal surfaces, Physical Review B, vol.29, issue.8, pp.4631-4676, 1984.
DOI : 10.1103/PhysRevB.29.4631

M. Foata and . Schützenberger, Nombres d'Euler et permutations alternantes Unpublished manuscript available at www.emis, 1971.

. Viennot, Interprétations combinatoires des nombres d'Euler et de Genocchi, Semin. Theor. Nombres (Univ. Bordeaux), vol.11, pp.1-94, 1981.

F. Leroux, G. Bergeron, and . Labelle, Combinatorial Species and Tree-like Structures, volume 67 of Encyclopedia of Mathematics and its Applications, 1998.

B. Reed and . Simon, Methods of Modern Mathematical Physics. II Fourier Analysis, Self-adjointness, 1975.

. Bloch, Sur la d??termination de l'??tat fondamental d'un syst??me de particules, Nuclear Physics, vol.7, pp.451-459, 1958.
DOI : 10.1016/0029-5582(58)90284-0

A. J. Michels and L. G. Suttorp, Diagrammatic analysis of adiabatic and time-independent perturbation theory for degenerate energy levels, Chemical Physics Letters, vol.58, issue.3, pp.385-393, 1978.
DOI : 10.1016/0009-2614(78)85058-1

Y. Dmitriev and O. V. Solnyshkina, Adiabatic perturbation theory for the degenerate case. III. Adiabatic formalism by Gell-Mann and low with an arbitrary switching function, International Journal of Quantum Chemistry, vol.39, issue.6, pp.543-553, 1988.
DOI : 10.1002/qua.560330606

S. Lindgren, B. Salomonson, and . Asén, The covariant-evolution-operator method in bound-state QED, Physics Reports, vol.389, issue.4, pp.161-261, 2004.
DOI : 10.1016/j.physrep.2003.09.004

. Ch, F. Brouder, and . Patras, Hyperoctahedral Chen calculus for effective Hamiltonians, J. Algebra, vol.322, pp.4105-4125, 2009.

. Viennot, Permutations ayant une forme donnee, Discrete Mathematics, vol.26, issue.3, pp.279-84, 1979.
DOI : 10.1016/0012-365X(79)90035-9
URL : http://doi.org/10.1016/0012-365x(79)90035-9

M. Frantz and R. L. Mills, Many-body basis for the optical model, Nuclear Physics, vol.15, pp.16-32, 1960.
DOI : 10.1016/0029-5582(60)90278-9

A. Bethe, B. H. Brandow, and A. G. Petscheck, Reference Spectrum Method for Nuclear Matter, Physical Review, vol.129, issue.1, pp.225-64, 1963.
DOI : 10.1103/PhysRev.129.225

H. Brandow, Linked-Cluster Expansions for the Nuclear Many-Body Problem, Reviews of Modern Physics, vol.39, issue.4, pp.771-828, 1967.
DOI : 10.1103/RevModPhys.39.771

. Olszewski, Combinatorical analysis of the Rayleigh-Schr??dinger perturbation theory based on a circular scale of time, International Journal of Quantum Chemistry, vol.78, issue.3, pp.784-801, 2004.
DOI : 10.1002/qua.10776

P. Stanley, Enumerative Combinatorics. Volume II, 1986.

. Rawlings, The ABC's of classical enumeration, Ann. Sci. Math. Quebec, vol.10, pp.207-242, 1986.

P. Stanley, Enumerative Combinatorics. Volume I, 1986.

-. Loday and M. O. Ronco, Order structure on the algebra of permutations and planar binary trees, Journal of Algebraic Combinatorics, vol.15, issue.3, pp.253-70, 2002.
DOI : 10.1023/A:1015064508594

P. Stanley, Theory and Application of Plane Partitions: Part 1, Studies in Applied Mathematics, vol.33, issue.1, pp.167-88, 1971.
DOI : 10.1002/sapm1971502167

. Chapoton, Alg??bres de Hopf des permutah??dres, associah??dres et hypercubes, Advances in Mathematics, vol.150, issue.2, pp.264-75, 2000.
DOI : 10.1006/aima.1999.1868

. Chapoton, Big??bres diff??rentielles gradu??es associ??es aux permuto??dres, associa??dres et hypercubes, Annales de l???institut Fourier, vol.50, issue.4, pp.1127-53, 2000.
DOI : 10.5802/aif.1787

. Kato, Perturbation Theory for Linear Operators, 1995.
DOI : 10.1007/978-3-662-12678-3

. Ch, G. Brouder, G. Panati, and . Stoltz, Gell-Mann and Low formula for degenerate unperturbed states, pp.1285-309, 2010.

. Ch, G. Brouder, G. Panati, and . Stoltz, Many-body Green function of degenerate systems, Phys. Rev. Lett, vol.103, p.230401, 2009.

. Goldstone, Derivation of the Brueckner Many-Body Theory, Proc. Roy. Soc, pp.267-79, 1957.
DOI : 10.1098/rspa.1957.0037

K. U. Gross, E. Runge, and O. Heinonen, Many-Particle Theory, 1991.

J. Lindgren and . Morrison, Atomic Many-Body Theory, 1986.
DOI : 10.1007/978-3-642-61640-2

R. P. Bloch and . Stanley, Sur la théorie des perturbations desétatsdesétats liés Chains in the Bruhat order, Nucl. Phys. J. Algebraic Combin, vol.6, issue.29, pp.329-47133, 1958.

K. Feil, R. M. Hutson, and . Kretchmar, Tree traversal and permutations, Congressus Numerantium, vol.172, pp.201-222, 2005.

. Ch, B. Brouder, A. Fauser, R. Frabetti, and . Oeckl, Quantum field theory and Hopf algebra cohomology, J. Phys. A: Math. Gen, vol.37, pp.5895-927, 2004.

. Ch and . Brouder, Quantum field theory meets Hopf algebra, Math. Nachr, vol.282, pp.1664-90, 2009.

B. Reed and . Simon, Methods of Modern Mathematical Physics. IV Analysis of Operators, 1978.

A. Agrachev and R. V. Gamkrelidze, The shuffle product and symmetric groups, Differential Equations, Dynamical Systems and Control Science, pp.365-82, 1994.

P. Schützenberger, Sur une propriété combinatoire des algèbres de lie libres pouvantêtrepouvantêtre utilisée dans unprobì eme de mathématiques appliquées, Séminaire Dubreil?Jacotin Pisot, p.59, 1958.

-. Thibon, F. Hivert, and J. Novelli, The algebra of binary search trees, 53 C. Reutenauer. Free Lie Algebras, pp.129-65, 1997.
URL : https://hal.archives-ouvertes.fr/hal-00622706

. L. Patras, Decent Algebra of a Graduated Bigebra, Journal of Algebra, vol.170, issue.2, pp.547-66, 1994.
DOI : 10.1006/jabr.1994.1352

N. Aguiar, K. Bergeron, and . Nyman, The peak algebra and the descent algebras of type B and D, Transactions of the American Mathematical Society, vol.356, issue.07, pp.2781-824, 2004.
DOI : 10.1090/S0002-9947-04-03541-X

J. Aguiar, J. Novelli, and . Thibon, Unital versions of the higher order peak algebras, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00823077