Mrwczyński, S; Müller, B, *Wigner functional approach to quantum field dynamics*,
Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 50 no. 12
(1994),
pp. 7542-7552 [pdf], [doi] .
**Abstract:**

*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 points 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 rollover phase transition. Finally, we briefly discuss the approximate methods for the evaluation of the Wigner functional that may be used to numerically simulate the initial value problem. © 1994 The American Physical Society.*