Secularly growing loop corrections in scalar wave background
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Springer
Received: June 8, Revised: August 18, Accepted: September 1, Published: October 5,
2020 2020 2020 2020
E.T. Akhmedova,b and O. Diatlykc a
Laboratory of High Energy Physics, Moscow Institute of Physics and Technology, Pervomaiskaya str., Dolgoprudny 141700, Russia b Institute for Theoretical and Experimental Physics, Bol’shaya Cheremushkinskaya str., 25, Moscow 117218, Russia c Faculty of Mathematics, National Research University Higher School of Economics, Usacheva str., 6, Moscow 119048, Russia
E-mail: [email protected], [email protected] Abstract: We consider two-dimensional Yukawa theory in the scalar wave background φ(t − x). If one takes as initial state in such a background the scalar vacuum corresponding to φ = 0, then loop corrections to a certain part of the Keldysh propagator, corresponding to the anomalous expectation value, grow with time. That is a signal to the fact that under the kick of the φ(t − x) wave the scalar field rolls down the effective potential from the φ = 0 position to the proper ground state. We show the evidence supporting these observations. Keywords: Nonperturbative Effects, Effective Field Theories, Renormalization Group ArXiv ePrint: 2004.01544
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)027
JHEP10(2020)027
Secularly growing loop corrections in scalar wave background
Contents 1 Introduction
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2 Action, modes and tree-level Green functions
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4 Loop corrections to the fermion propagators 4.1 One loop correction to the Keldysh propagator for fermions 4.2 One loop corrections to vertexes
12 13 15
5 Dyson equation for the exact Keldysh propagator for scalars 5.1 Stationary solution of the Dyson-Schwinger equation
15 17
6 Conclusions
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A Calculation of one loop corrections to the Keldysh Green function for scalars 23 B Derivation of the Dyson-Schwinger equation for the scalar Keldysh propagator 27 C Some comments about one loop corrections to the Keldysh propagator for scalars in the case of constant classical background field 29 D Calculation of loop corrections in 2+1 dimensions
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Introduction
The aim of quantum field theory is to find the response of a system to external perturbations: in particular, to find correlation functions or, more generically, correlations between an external influence on the system and its backreaction on it. In classical field theory correlation functions are solutions of equations of motion. In quantum field theory one also should take into account quantum fluctuations, i.e. calculate loop corrections to the tree-level correlation functions. Usually one treats quantum fluctuations using Feynman diagrammatic technique. It implicitly assumes that external perturbations do not change the initial state of the theory, i.e. the system remains stationary [1–3]. However, strong background fields usually
–1–
JHEP10(2020)027
3 Loop corrections to the boson correlation functions 3.1 One loop corrections to the one point scalar correlation functions 3.2 One loop correct
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