Quantum Field Theory Approach to the Analysis of One-Step Models

During development of methods for stochastization of one-step processes the attention was focused on obtaining the stochastic equations in the form of the Langevin, since this form of stochastic equations is most usual in the construction and study of one-step processes models. When applying the method there is the problem of justifying the transition from master equation to the Fokker-Planck equation for the different versions of the model. However, the forms of partial differential equations (master equation and the Fokker-Planck equation) wider description of the model to researchers. It is proposed to treat these equations with the help of perturbation theory in the framework of quantum field theory. For this purpose the methodology was described and the analytical software complex was constructed to write down put the main kinetic equation in the operator form in the Fock representation. To solve the resulting equation the software complex generates Feynman diagrams for the corresponding order of perturbation theory. The FORM system was applied as a system of symbolic computation. Selecting FORM as the CAS is reasonable because that the given computer algebra system allows for symbolic computation, using the resources of high-performance computing. In particular, it is possible to use parallel computing technologies such as OpenMP and MPI.

algebraic biology, master equation, Fokker-Planck equation, population models, computer algebra software, FORM system, stochastic differential equations