Description of Photon Field in Dynamics Simulation of Bound States Based on Quantum Field Theory

Abstract

Quantum field theory (QFT) is considered to be most correct for the description of quantum systems. For the reason, we study local physical quantities defined in QFT, such as local polarizability, local conductivity, local spin torque [1–4]. In these works, for quantum states, we used wave packets derived by first principles calculation based on quantum mechanics. To treat states and physical quantities consistently, quantum systems should be treated in QFT. Hence, we are developing a first principles calculation program package based on quantum electrodynamics (QED). We name this program package QEDynamics [5]. The purpose of this program package is to study time evolution of quantum systems consisting of molecules or condensed matter. This challenge has two points of difficulties. One is the non-perturbativity, and the other is the time evolution of quantum systems. The formulation of QFT has been developed in a perturbative method. Hence perturbative calculations are widely used. For non-perturbative systems i.e. bound states, many methods are explored, lattice quantum chromodynamics, NRQED [6], Bethe-Salpeter method, and so on. All methods have various advantages and disadvantages, and hence we should be careful with the treatment of non-perturbative systems. Moreover, in most perturbative calculations, the existence of asymptotic states is assumed and the time integration from −∞ to∞ is performed for calculations, such as cross section. Thus the time evolution i.e. the study of nonequilibrium systems is restricted in specific cases. In literature, nonequilibrium systems are studied by Boltzmann equation, closed time path formalism [7], thermo field dynamics [8] and so on. We solve directly Heisenberg equations of field operators in QED in the present version of QEDynamics for the study of time evolution. In computational simulations, operators are difficult to handle. In our program, the evolution of the operators is calculated as the transition between modes prepared by the method of first principles computations of quantum structures. This mode expansion is based on the method used in Furry picture. This choice of the expansion functions of field operator has an advantage representing bound states. In this article, we show the present status of our program. In particular, the computation method of the evolution of photon fields are explained. Hence most other detail information cannot be mentioned in this article. For the information, please see Ref. [5].