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On the status of perturbation theory

Published online by Cambridge University Press:  01 April 2007

THIERRY PAUL
THIERRY PAUL*
Affiliation:
Départemant de Mathématiques et Applications, Ecole Normale Supérieure and C.N.R.S., 45 rue d'Ulm, F – 75230 Paris Cedex 05
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Extract

Perturbation theory has always been an important component of the natural sciences. From celestial mechanics to the quantum theory of fields, it has always played a central role, which this little note sets out to analyse briefly. We will show, in particular, how its epistemological position has changed from being just a ‘tool’ to being the basis of definition for objects in quantum field theory.

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Paper
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Mathematical Structures in Computer Science , Volume 17 , Issue 2 , April 2007 , pp. 277 - 288
Copyright
Copyright © Cambridge University Press 2007

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References

Bachelard, G. (1969) Essai sur la connaissance approchée, Vrin, Paris.Google Scholar
Born, M. (1925) Vorlesungen über Atommechanik, Springer, Berlin. (English translation: The mechanics of the atom, Ungar, New York, 1927.)Google Scholar
Born, M. and Jordan, P. (1930) Elementare Quantenmechanik (zweiter Band der Vorlesungen über Atommechanik), Springer.Google Scholar
Brillouin, M. (1988) Préface to: Schrödinger, E. Mémoires sur la mécanique Quantique, Gabayaris.Google Scholar
Chirikov, B. (1979) Phys. Rep. 52 26.CrossRefGoogle Scholar
Connes, A. and Kreimer, D. (1998) Hopf algebra, renormalization and noncommutative geometry. Com. Math. Phys. 199 203.Google Scholar
Fermi, E. (1930) La théorie du rayonnemnt.Annales de l'Institut H. Poincaré 1 53–74.Google Scholar
Gallavotti, G. (private communication).Google Scholar
Graffi, S. and Paul, T. (1987) The Schrödinger equation and canonical perturbation theory. Com. Math. Phys. 108 25–40.CrossRefGoogle Scholar
Gimm, J. and Jaffe, A. (1987) Quantum physics: a functional integral point of view, Springer.Google Scholar
Heisenberg, W. (1925) Matrix mechanik. Zeitscrift für Physik 33 879–893.Google Scholar
Jankélévitch, V. (1950) Philosophie première. Introduction à une philosophie du presque, Gallimard.Google Scholar
Kolmogorov, N. (1954) The general theory of dynamical systems and classical mechanics. Proceedings of the International Congress of Mathematicians, Amsterdam 1954, North-Holland.Google Scholar
Longo, G. (2005) Savoir critique et savoir positif: l'importance des résultats négatifs. Intellectica 40 (1). (English translation: Information Technology and Media, web-page of the European Commission.)Google Scholar
Poincaré, H. (1987) Les méthodes nouvelles de la mécanique céleste, Volume 3, Blanchard, Paris.Google Scholar
Schrödinger, E. (1926) Quantisierung und eigenvalues. Ann. der Physics 79.Google Scholar
Streater, R. and Whitgman, A. (1964) Spin, statistics and all that, Benjamin.Google Scholar
Weinberg, S. (2002) The quantum theory of fields, Vol. 1, Cambridge University Press.Google Scholar