Effective non - perturbative real - time dynamics of soft modes in hot gauge theories
نویسنده
چکیده
We derive, from first principle, the Fokker-Planck equation describing the non-perturbative real-time evolution of a gauge field at high temperatures on the spatial scale (g 2 T) −1 and the time scale (g 4 T) −1 , where g is the gauge coupling and T is the temperature. The knowledge of the effective dynamics on such spatial and time scales is crucial for the understanding and quantitative calculation of the baryon number violation rate at high temperatures in the electroweak theory. The Fokker-Planck equation, which describes the diffusive motion of soft components of the gauge field in the space of field configurations, is shown to be gauge-invariant and consistent with the known thermodynamics of soft gauge modes. We discuss the ways the Fokker-Planck equation can be made useful for numerical simulations of long-distance dynamics of hot gauge theories.
منابع مشابه
Effective theory for real-time dynamics in hot gauge theories
For a high temperature non-Abelian plasma, we reformulate the hard thermal loop approximation as an effective classical thermal field theory for the soft modes. The effective theory is written in local Hamiltonian form, and the thermal partition function is explicitly constructed. It involves an ultraviolet cutoff which separates between hard and soft degrees of freedom in a gauge-invariant way...
متن کاملHow to compute the anomalous baryon number violation at high temperature
We present an effective classical theory for the soft modes of a high temperature non-Abelian plasma. This theory is formulated in local Hamiltonian form, and is well suited for numerical non-perturbative studies of the real-time dynamics. It includes the short-range dynamics in the hard thermal loop approximation, with appropriate corrections which take care of the cutoff effects in a gauge-in...
متن کاملNon-perturbative Aspects of Hot Qcd
I discuss some non-perturbative aspects of hot gauge theories as related to the unscreened static magnetic interactions. I first review some of the infrared divergences which cause the breakdown of the perturbation theory. Then I show that kinetic theory, as derived from quantum field theory, is a powerful tool to construct effective theories for the soft modes, which then can be treated non-pe...
متن کاملNon-equilibrium Dynamics of Hot Abelian Higgs Model
Depending on its details, the electroweak phase transition may explain the observed baryon asymmetry in the Universe. Although static equilibrium properties such as the phase structure of the theory have been determined to high accuracy with numerical lattice simulations, much less is known about non-equilibrium dynamics, or even real-time correlators in equilibrium. The reason is that to calcu...
متن کاملEffective theories for real-time correlations in hot plasmas
We discuss the sequence of effective theories needed to understand the qualitative, and quantitative, behavior of real-time correlators 〈A(t)A(0)〉 in ultrarelativistic plasmas. We analyze in detail the case whereA is a gauge-invariant conserved current. This case is of interest because it includes a correlation recently measured in lattice simulations of classical, hot, SU(2)-Higgs gauge theory...
متن کامل