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Ward Schwinger Dyson and resurgence

Abstract : This thesis is a contribution to the problem of extracting non-perturbative information from quantum field theory in the absence of supersymmetry or integrability conditions. The resurgence theory is a very promising candidate for this. The hard point in applying resurgence to quantum field theory is that we don't have the entire asymptotic series. One can hardly calculate its first terms, although sometimes heroically, much less guess its asymptotics. The Schwinger Dyson equations associated with renormalization offer a solution to this shortage : written in terms of renormalized quantities, the functional equations involve differential equations forthe abnormal dimensions. At this point, the resurgence can strike. Our result is therefore to extract non-perturbative contributions with anomalous dimensions. These data lead in principle to a non-perturbative expression of the propagator by the integration of renormalization equations. The main result of this work is therefore the introduction of Ward Schwinger Dyson's method and its resurgent characterization. The first allows to formulate Schwinger Dyson equations where also the vertices are renormalized,opening the study to complete interactive theories ; the second brought to light the complex structure of singularities which, for the moment, prevents a complete integration of Green functions. While for the linear and nonlinear Wess-Zumino Yukawa model the hierarchy of trans series allows an efficient organizational framework for computations, in the fully nonlinear and renormalized case this is hampered due to the irrational value powers in the trans-expansion of the series.
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Submitted on : Friday, September 9, 2022 - 12:36:10 PM
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  • HAL Id : tel-03773614, version 1

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Enrico Russo. Ward Schwinger Dyson and resurgence. High Energy Physics - Theory [hep-th]. Sorbonne Université, 2020. English. ⟨NNT : 2020SORUS458⟩. ⟨tel-03773614⟩

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