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Summation methods play a very important role in quantum field theory because all perturbation series are divergent and the expansion parameter is not always small.
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A. Duncan, H. F. Jones, Convergence proof for optimized δ \delta expansion: Anharmonic oscillator, Phys. Rev. D 47 (1993) 2560-2572
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C. M. Bender, A. Duncan, H. F. Jones, Convergence of the optimized δ \delta expansion for the connected vacuum amplitude: Zero dimensions, Phys. Rev. D 49 (1994) 4219-4225
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R. Guida, J. Zinn-Justin, 3D Ising Model: The Scaling Equation of State, Nucl. Phys. B 489 (1997) 626-652
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E. Braaten, E. Radescu, Convergence of the Linear δ \delta Expansion in the Critical O ( N ) O(N) Field Theory, Phys. Rev. Lett. 89 (2002) 271602 [4 pages]
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F. de Souza Cruz, M.B. Pinto, R.O. Ramos, P. Sena, Higher-order evaluation of the critical temperature for interacting homogeneous dilute Bose gases, Phys. Rev. A 65 (2002) 053613 [24 pages]
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J. Zinn-Justin, Quantum Field Theory and Critical Phenomena: fourth edition, Oxford University Press, Oxford, 2002
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H. Kleinert, W. Janke, Convergence behavior of variational perturbation expansion — A method for locating Bender-Wu singularities, Phys. Lett. A 206 (1995) 283-289
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B. Bellet, P. Garcia, A. Neveu, Convergent sequences of perturbative approximations for the anharmonic oscillator I, Int. J. Mod. Phys. A 11 (1996) 5587-5606
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R Guida, K Konishi, H Suzuki, Improved Convergence Proof of the Delta Expansion and Order Dependent Mappings, Ann. Phys. 249 (1996) 109-145
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J.L. Kneur, M.B. Pinto, R.O. Ramos, Asymptotically improved convergence of optimized perturbation theory in the Bose-Einstein condensation problem, Phys. Rev. A 68 (2003) 043615 [30 pages]
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J. L. Kneur, M. B. Pinto, R. O. Ramos Critical and tricritical points for the massless 2D Gross–Neveu model beyond large N N , Phys. Rev. D 74 (2006) 125020 [18 pages]
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J. L. Kneur, M. B. Pinto, R. O. Ramos, E. Staudt, Emergence of tricritical point and liquid-gas phase in the massless 2+1 dimensional Gross–Neveu model, Phys. Rev. D 76 (2007) 045020 [19 pages]
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