Methods of Efimov Nonlocal and Nonpolynomial Quantum Field Theory in the Theory of Stochastic Partial Differential Equations
Семинары
Cеминар «Теория квантового поля»
Дата и время: четверг, 25 января 2018 г., в 15:00
Место: Конференц-зал им. Блохинцева (4-й этаж), Лаборатория теоретической физики им. Н.Н. Боголюбова
Тема семинара: «Methods of Efimov Nonlocal and Nonpolynomial Quantum Field Theory in the Theory of Stochastic Partial Differential Equations»
Докладчик: Stanislav Ogarkov (Dukhov Research Institute of Automatics, Moscow Institute of Physics and Technology)
Аннотация:
The main ideas of this presentation are the revision of the Efimov quantum field theory (QFT), a brief recapitulation of the theory of stochastic partial differential equations (SPDEs; in particular, the critical dynamics equations and the equations of the stochastic theory of turbulence), and the synthesis of these two directions: the application of the Efimov QFT methods in the SPDEs theory. In the first part of the presentation, the Efimov QFT of the one component scalar field in D-dimensional spacetime is revisited. The expansion of the S-matrix for different interaction Lagrangians and Gaussian propagators with ultraviolet form factors is studied. The expansion of the S-matrix in the form of a grand canonical partition function of some D+N-dimensional (N ≥ 1) classical gas with interaction is obtained. Then, the functional Schwinger–Dyson and Schrödinger equations for the S-matrix in Efimov representation are derived. The asymptotic solutions of the Schwinger–Dyson equation are obtained. Finally, the connection with functional and holographic renormalization groups is made. In the second part of the presentation, as a brief recapitulation of the theory of SPDEs, the critical dynamics equations, the equations of the turbulent advection, the hydrodynamics equations and the Kardar–Parisi–Zhang equation are considered. In addition, the procedure for constructing of the QFT model for the wide class of SPDEs is given. In the final part of the presentation, several scenarios for the application of methods of Efimov QFT in the theory of SPDEs are presented. The field theoretic generating functional (in turbulence and critical dynamics) in terms of a grand canonical partition function of some classical gas is calculated. Finally, one more interesting scenario, devoted to the SPDEs with nongaussian random force is given.