Perturbation theory at large order. I. The <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>φ</mi></mrow><mrow><mn>2</mn><mi>N</mi></mrow></msup></mrow></math></span> interaction

E. Brézin; J. C. Le Guillou; J. Zinn-Justin

doi:10.1103/PhysRevD.15.1544

Perturbation theory at large order. I. The $φ^{2 N}$ interaction

E. Brézin, J. C. Le Guillou, and J. Zinn-Justin

Phys. Rev. D 15, 1544 – Published 15 March 1977

Abstract

A new method for calculating the large orders of perturbation theory in quantum field theories has been discussed recently by Lipatov. We show that the same method applied to anharmonic oscillators in quantum mechanics allows one to rederive and generalize results previously obtained by Bender and Wu. We have also verified and generalized Lipatov's results to the case of an internal $O (n)$ symmetry. These results show the divergence of the Wilson-Fisher $ε$ expansion and indicate its Borel summability which is used for critical exponents. Similarly, the Callan-Symanzik functions for the $φ^{4}$ theory in three dimensions are characterized.

Received 13 October 1976

DOI:https://doi.org/10.1103/PhysRevD.15.1544

Authors & Affiliations

E. Brézin, J. C. Le Guillou^*, and J. Zinn-Justin

Service de Physique Théorique, Centre d' Etudes Nucleaires de Saclay, BP N° 2—91190 Gif-sur-Yvette, France

^*Permanent address: Laboratoire de Physique Théorique et Hautes Energies, Tour 16, Université Paris VI 75230 Paris Cedex 05, France.

Perturbation theory at large order. II. Role of the vacuum instability

E. Brézin, J.-C. Le Guillou, and J. Zinn-Justin

Phys. Rev. D 15, 1558 (1977)

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Vol. 15, Iss. 6 — 15 March 1977

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