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Equal-time approach to real-time dynamics of quantum fields

by Robert Ott, Torsten V. Zache, and Jürgen Berges

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Robert Ott
Submission information
Preprint Link: scipost_202204_00043v1  (pdf)
Date accepted: 2022-09-02
Date submitted: 2022-04-29 00:44
Submitted by: Ott, Robert
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Atomic, Molecular and Optical Physics - Theory
  • High-Energy Physics - Theory
  • Quantum Physics
Approach: Theoretical


We employ the equal-time formulation of quantum field theory to derive effective kinetic theories, first for a weakly coupled non-relativistic Bose gas, and then for a strongly correlated system of self-interacting N-component fields. Our results provide the link between state-of-the-art measure- ments of equal-time effective actions using quantum simulator platforms, as employed in Refs. [1, 2], and observables underlying effective kinetic or hydrodynamic descriptions. New non-perturbative approximation schemes can be developed and certified this way, where the a priori time-local formu- lation of the equal-time effective action has crucial advantages over the conventional closed-time-path approach which is non-local in time.

Published as SciPost Phys. 14, 011 (2023)

Reports on this Submission

Anonymous Report 2 on 2022-8-15 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:scipost_202204_00043v1, delivered 2022-08-15, doi: 10.21468/SciPost.Report.5537


Usually (e.g., such as expounded in Calzetta and Hu, Nonequilibrium Quantum Field Theory, CUP (2008)) nonequilibrium quantum fields are described in terms of unequal time correlations. This raises some issues of principle (for example, whether causality is enforced when deriving kinetic theory from quantum field theory) and most importantly does not match actual experimental practice. This paper shows that it is possible to develop nonequilibrium quantum field theory completely in terms of equal time correlations. The paper is highly formal - essentially it translates to the language of equal time correlations everything one already knows about the unequal time ones- but opens up new avenues in nonequilibrium quantum field theory and will be useful to the community.

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

Anonymous Report 1 on 2022-6-22 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:scipost_202204_00043v1, delivered 2022-06-22, doi: 10.21468/SciPost.Report.5268


1. This is a very detailed well-structured paper written in a logical way.
2. It contains important and necessary details to help readers to go through the derivations.
3. The notations are all set and explained in the Section II.
4. The key equations are illustrated with the Feynman diagrams.
5. General theory is illustrated with several examples including both perturbative and non-perturbative (large N) approaches.
6. The Section VI is devoted to the measurement protocol to be implemented with the cold-atom simulators.
7. Appendices provide sufficient details for the experts.


This is a very interesting technical paper addressing general questions of the quantum field theoretical approach to the out-of equilibrium quantum systems. Besides, it addresses the measurement protocols to be implemented with cold-atom quantum simulators. My personal opinion is that the paper will attract an attention of different target groups from PhD students who learn many-body techniques to the experts actively working in the field. I think that the paper is well written and would not suggest any changes at present stage.

  • validity: high
  • significance: high
  • originality: high
  • clarity: high
  • formatting: excellent
  • grammar: excellent

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