SciPost Submission Page
Relaxation time approximation revisited and non-analytical structure in retarded correlators
by Jin Hu
Submission summary
| Authors (as registered SciPost users): | Jin Hu |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202507_00030v2 (pdf) |
| Date submitted: | Dec. 1, 2025, 1:07 p.m. |
| Submitted by: | Jin Hu |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Phenomenological |
Abstract
In this paper, we give a rigorous mathematical justification for the relaxation time approximation (RTA) model. We find that only the RTA with an energy-independent relaxation time can be justified in the case of hard interactions. Accordingly, we propose an alternative approach to restore the collision invariance lacking in traditional RTA. Besides, we provide a general statement on the non-analytical structures in the retarded correlators within the kinetic description. For hard interactions, hydrodynamic poles are the long-lived modes. Whereas for soft interactions, commonly encountered in relativistic kinetic theory, the gapless eigenvalue spectrum of linearized collision operator leads to gapless branch-cuts. We note that particle mass and inhomogeneous perturbations would complicate the above-mentioned non-analytical structures.
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List of changes
- In the new version, in the second paragraph of the Introduction section, a citation to and comment on ref. [15] have been added after the word "Also". 2.In the new version, a citation to ref. [20] has been added to the second sentence of the fourth paragraph in the Introduction section. 3.In the new version, citations to Marle's relevant works, ref. [23] and [24], have been added to the fifth and sixth sentences of the fourth paragraph in the Introduction section. 4.In the new version, a comment has been added below Eq. (9): "It should be noted that the corresponding integrals within the definitions should converge, which excludes very large values for \alpha". 5.In the new version, the first sentence of the last paragraph in Section III.C has been revised to: "The observer argument above can provide an equivalent justification for reconciling the seemingly contradictory aspects ..." 6.In the new version, the second sentence of the paragraph above Eq. (28) has been revised to: "We first assume that \cos\theta, regarded as an operator in momentum-space functions ..." 7.In the new version, the last sentence of the paragraph below Eq. (30) has been revised to: "Ultimately, the resulting branch-cut structure seemingly reproduces the result for nonzero k given in ...".