Applicability of the Wigner functional approach to evolution of quantum fields

Abstract

Abstract. Evolution of highly excited quantum field is considered in the framework of Keldysh formalism . It is demonstrated that leading order (LO) term of semiclassical approximation appears as well-known Classical Statistical Approximation (CSA). In simple case of spatially homogeneous scalar field analytical expressions for leading and next-toleading (NLO) order are presented. It is shown that the range of applicability of CSA strongly depends on the properties of the initial state of the system.

Quantum corrections to the classical statistical approximation for the expanding quantum field

“…Let us note that from the expression (32) we see that significant contributions form the NLO terms correspond to the limit of small A. Therefore for the CSA approximation to be valid we need to choose the Wigner distributions with large initial amplitudes φ m (α, p) and fast decaying tales [16,17].…”

“…In the first work we described the systematic procedure of computing quantum corrections in the framework of KS formalism, derived analytical expressions for pressure relaxation in the scalar field model and wrote down explicit expressions for the NLO corrections for one-point and two-point correlation functions. In the second paper [17] we derived analytical expressions for the mean field, energy and pressure of the homogeneous scalar field in the static geometry and discussed the critical role of the character of initial conditions for applicability of the CSA approximation.…”

Comments on the adiabatic theorem

“…This approach was initiated by Julian Schwinger [4] and further developed by L. V. Keldysh [5]. Schwinger-Keldysh approach has many applications in condensed matter physics [6][7][8][9][10][11][12][13][14][15], cosmology [16][17][18][19][20][21][22][23][24][25][26], ultra relativistic heavy ion collisions [27][28][29][30][31], non-stationary phenomena in the strong background field [32][33][34][35] and so on.…”

Semiclassical Approximation meets Keldysh-Schwinger diagrammatic technique: Scalar $φ^4$

“…Also, this technique can be used for the systematic evaluation of thermodynamical and transport properties of the quantum systems at the thermal equilibrium [3,4]. Another way to deal with the nonequilibrium initial state comes from the physical intuition and based on the assumption that at high energies and/or high occupation number the dynamics of the quantum fields is a semiclassical one, so one can use the classical equations of motion [10,11,[13][14][15][16][17][18]24]. In order to complete this approach, one should make additional assumptions about ensemble which is used for the averaging of observables.…”

“…Aim of this work is to unify all these approaches and demonstrate that both Keldysh-Schwinger diagram technique and classical statistical approach are two facets of one general way to deal with nonequilibrium quantum fields. In the previous works of one of the authors [16][17][18], the Classical Statistical Approximation was examined in details for the scalar field theory. It was shown how this approach arises in the leading order of the semiclassical (in ) expansion.…”