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arXiv:2605.22822

Bottom-up open EFT for non-Abelian gauge theory with dynamical color environment

Yoshihiko Abe, Kanji Nishii

hep-thhep-phquant-phSubmitted May 21, 2026• Announced May 22, 2026• Revised Sep 15, 2026 (v2)
v1 · May 21, 2026v2 · Sep 15, 2026
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Abstract

We develop a bottom-up open effective field theory (EFT) for non-Abelian gauge theories within the Schwinger--Keldysh formalism. Instead of integrating out the environment completely and starting from a nonlocal influence functional, we retain the slow environmental response variables explicitly and construct a local system-environment EFT. The environmental sector is described by a dynamical color-frame variable, Stückelberg-like field, and an associated color-current sector, which gives the nontrivial interactions and dissipation between the system and the environment. The resulting construction provides a gauge-covariant Markov embedding of nonlocal and non-Markovian color response. After integrating out the retained environmental variables with retarded boundary conditions, the reduced system theory acquires nonlocal dissipative kernels and stochastic sources. We show that the hard thermal loop response arises naturally as a particular realization of the retained environmental response. Our framework provides a local open-EFT description of color transport, memory effects, and fluctuation-dissipation structure in non-Abelian plasmas, and offers a systematic starting point for dissipative Yang--Mills EFTs with dynamical environments.

Comments
52 pages, 1 figure. Version to appear in JHEP

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We present a perturbative derivation of the generalized Langevin equation starting from a relativistic quantum field theory at finite temperature. Considering a complex scalar field coupled to a thermal mediator, we use a collective field formulation (Hubbard-Stratonovich transformation) to decouple the non-linear density constraint associated with a localized composite degree of freedom. By performing a saddle-point expansion and explicitly integrating out the collective fluctuations, we obtain the dynamic response kernel for the macroscopic center-of-mass coordinate. We show that localizing the density spontaneously breaks translational invariance, naturally generating a harmonic restoring force that results in an Ornstein-Uhlenbeck process. Furthermore, we resolve the vanishing friction paradox of the free-field limit by employing a resummed Dyson-Schwinger approach. We explicitly demonstrate that the thermal width of the dressed propagator generates finite Ohmic dissipation via Landau damping of the Källén-Lehmann spectral functions. This work provides a transparent, effective field theory bridge between microscopic thermal quantum fields and macroscopic open quantum systems.
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