SciPost logo

SciPost Submission Page

Real-time dynamics of the $O(4)$ scalar theory within the fRG approach

by Yang-yang Tan, Yong-rui Chen, Wei-jie Fu

Submission summary

As Contributors: Wei-jie Fu
Arxiv Link: (pdf)
Date submitted: 2021-10-20 03:59
Submitted by: Fu, Wei-jie
Submitted to: SciPost Physics
Academic field: Physics
  • High-Energy Physics - Phenomenology
Approach: Theoretical


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 $z\simeq 2.023$.

Current status:
Editor-in-charge assigned

Author comments upon resubmission

We thank the referee for his suggestions in the second report, which we have taken into account in the revised version.

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.

Reports on this Submission

Anonymous Report 1 on 2021-10-21 (Invited 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.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

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.

Login to report or comment