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The Lipatov argument (1980)

Spencer, Thomas

Springer

Communications in mathematical physics 74 (1980), S. 273-280

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ISSN: 1432-0916

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics , Physics

Notes: Abstract Lipatov's argument gives a formula for evaluating asymptotically the large order perturbation coefficients for the anharmonic oscillator or (φ4) quantum field models. We give a partial justification of the argument which enables us to prove that the radius of convergence of the Borel transform of the pressure for lattice φ4 models given by $$\exp \left[ {\mathop {\inf }\limits_\phi \left\{ {\tfrac{1}{2}\sum\limits_j {\left[ {(\nabla \phi )^2 (j) + \phi (j)^2 } \right] - \log } \sum {\phi (j)^4 } } \right\} - 2} \right].$$

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01952890

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