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Alien calculus and a Schwinger–Dyson equation: two-point function with a nonperturbative mass scale
Bellon, Marc P. ; Clavier, Pierre J.
Letters in mathematical physics, 2018-02, Vol.108 (2), p.391-412
[Peer Reviewed Journal]
Dordrecht: Springer Netherlands
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Title:
Alien calculus and a Schwinger–Dyson equation: two-point function with a nonperturbative mass scale
Author:
Bellon, Marc P.
;
Clavier, Pierre J.
Subjects:
Calculus
;
Complex Systems
;
Field theory
;
Geometry
;
Group
Theory and Generalizations
;
High Energy Physics - Theory
;
Mathematical analysis
;
Mathematical and Computational Physics
;
Mathematical Physics
;
Physics
;
Physics and Astronomy
;
Quantum field theory
;
Quantum theory
;
Singularities
;
Theoretical
Is Part Of:
Letters in mathematical physics, 2018-02, Vol.108 (2), p.391-412
Description:
Starting from the Schwinger–Dyson equation and the
renormalization
group
equation for the massless Wess–Zumino model, we compute the dominant nonperturbative contributions to the anomalous dimension of the theory, which are related by alien calculus to singularities of the Borel transform on integer points. The sum of these dominant contributions has an analytic expression. When applied to the two-point function, this analysis gives a tame evolution in the deep euclidean domain at this approximation level, making doubtful the arguments on the triviality of the quantum field theory with positive β -function. On the other side, we have a singularity of the propagator for timelike momenta of the order of the
renormalization
group
invariant scale of the theory, which has a nonperturbative relationship with the
renormalization
point of the theory. All these results do not seem to have an interpretation in terms of semiclassical analysis of a Feynman path integral.
Publisher:
Dordrecht: Springer Netherlands
Language:
English
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