TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.20.1.020
TI  - Relaxation time approximation revisited and non-analytical structure in retarded correlators
PY  - 2026/01/26
UR  - https://scipost.org/SciPostPhys.20.1.020
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 20
IS  - 1
SP  - 020
A1  - Hu, Jin
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.20.1.020,
	title={{Relaxation time approximation revisited and non-analytical structure in retarded correlators}},
	author={Jin Hu},
	journal={SciPost Phys.},
	volume={20},
	pages={020},
	year={2026},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.20.1.020},
	url={https://scipost.org/10.21468/SciPostPhys.20.1.020},
}