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Real-time dynamics of the $O(4)$ scalar theory within the fRG approach
by Yang-yang Tan, Yong-rui Chen, Wei-jie Fu
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Wei-jie Fu · Yang-yang Tan |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2107.06482v3 (pdf) |
| Date accepted: | 2021-12-08 |
| Date submitted: | 2021-10-20 03:59 |
| Submitted by: | Fu, Wei-jie |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
In this paper, the real-time dynamics of the $O(4)$ scalar theory is studied within the functional renormalization group formulated on the Schwinger-Keldysh closed time path. The flow equations for the effective action and its $n$-point correlation functions are derived in terms of the "classical" and "quantum" fields, and a concise diagrammatic representation is presented. An analytic expression for the flow of the four-point vertex is obtained. Spectral functions with different values of temperature and momentum are obtained. Moreover, we calculate the dynamical critical exponent for the phase transition near the critical temperature in the $O(4)$ scalar theory in $3+1$ dimensions, and the value is found to be $z\simeq 2.023$.
Author comments upon resubmission
List of changes
1) Minor modification for the text on page 14 is made.
2) We have modified the discussion in the paragraph below Eq.(21), and a new reference (arXiv: 1611.07301) is added.
Published as SciPost Phys. 12, 026 (2022)
Reports on this Submission
Report
I thank the authors for considering my suggestions.
I am not convinced that the formulation concerning "thermal equilibrium" after Eq. (21) is completely correct, but this issue will probably have to be resolved by additional studies in the future. However, it is now clearly formulated what was done in the manuscript.
I therefore recommend publication without further changes.
Author: Wei-jie Fu on 2021-10-21 [id 1871]
(in reply to Report 1 on 2021-10-21)We thank the referee for the recommendation of publication.
We think that the referee still has the question whether it is adequate to regulate only the real part of the 2-point functions in thermal equilibrium. Although this is not quite relevant to the main subject in this manuscript, we would like to address it more clearly.
We think that the answer is "yes". The reason is due to the fact that in thermal equilibrium, the real and imaginary parts are not independent, while they are related to each other through a principal value integral, as shown in e.g., Eq.(B7) and Eq.(B8) in Appendix B. This is also reflected by the fluctuation-dissipation relation.
We hope that this issue is addressed clearly now. Thanks.