Applicability of the Wigner functional approach to evolution of quantum fields

Wigner functional of fermionic fields

The Wigner function, which provides a phase-space description of quantum systems, has various applications in quantum mechanics, quantum kinetic theory, quantum optics, radiation transport and others. The concept of Wigner function has been extended to quantum fields, scalar and electromagnetic. Then, one deals with the Wigner functional which gives a distribution of field and its conjugate momentum. We introduce here the Wigner functional of fermionic fields of the values in a Grassmann algebra. Properties of the functional are discussed and its equation of motion, which is of the Liouville's…

The Subtleties of the Wigner Function Formulation of the Chiral Magnetic Effect

We assess the applicability of the Wigner function formulation in its present form to the chiral Magnetic Effect and noted some issues regarding the conservation and the consistency of the electric current in the presence of an inhomogeneous and time dependent axial chemical potential. The problems are rooted in the ultraviolet divergence of the underlying field theory associated with the axial anomaly and can be fixed with the Pauli-Villars regularization of the Wigner function.

Wigner Functional Approach to Quantum Field Dynamics

We introduce the Wigner functional representing a quantum field in terms of the field amplitudes and their conjugate momenta. The equation of motion for the functional of a scalar field point out the relevance of solutions of the classical field equations to the time evolution of the quantum field. We discuss the field in thermodynamical equilibrium and find the explicit solution of the equations of motion for the so-called ``roll-over'' phase transition. Finally, we briefly discuss the approximate methods for the evaluation of the Wigner functional that may be used to numerically simulate the…

Wigner Functionals and their Dynamics in Quantum-Field-Theory

We reformulate time evolution of systems in mixed states in terms of the classical observables of correlators using the Weyl correspondence rule. The resulting equation of motion for the Wigner functional of the density matrix is found to be of the Liouville type. To illustrate the methods developed, we explicitly consider a scalar theory with quartic self-interaction and derive the short time behaviour with the non-interacting thermal density matrix as initial condition. In the scalar case, the complete correlator hierarchy is studied and restrictions are derived for spatially homogeneous ini…

Klein-Gordon方程在真空和等离子体中产生粒子对的适用性

Applicability of the Klein-Gordon equation for pair production in vacuum and plasma

本文通过Wigner变换比较Klein-Gordon与Dirac理论在真空和等离子体中的粒子对产生率，评估无自旋近似的适用性，发现适中频率下条件满足时两者吻合良好。

The Color Glass Condensate density matrix: Lindblad evolution, entanglement entropy and Wigner functional

We introduce the notion of the Color Glass Condensate (CGC) density matrix $\hatρ$. This generalizes the concept of probability density for the distribution of the color charges in the hadronic wave function and is consistent with understanding the CGC as an effective theory after integration of part of the hadronic degrees of freedom. We derive the evolution equations for the density matrix and show that the JIMWLK evolution equation arises here as the evolution of diagonal matrix elements of $\hatρ$ in the color charge density basis. We analyze the behavior of this density matrix under high …