Abstract
In this paper, the real-time dynamics of the O(4)O(4) scalar theory is studied within the functional renormalization group formulated on the Schwinger-Keldysh closed time path. The flow equations for the effective action and its nn-point correlation functions are derived in terms of the "classical'' and "quantum’’ fields, and a concise diagrammatic representation is presented. An analytic expression for the flow of the four-point vertex is obtained. Spectral functions with different values of temperature and momentum are obtained. Moreover, we calculate the dynamical critical exponent for the phase transition near the critical temperature in the O(4)O(4) scalar theory in 3+13+1 dimensions, and the value is found to be z\simeq 2.023z≃2.023.
Highlights
The past years have seen rapid progress in our understanding of the strongly correlated physics and its in-medium effects in the context of Euclidean field theories at finite temperature and density, e.g., QCD on a discretized lattice of Euclidean space and time [1, 2], functional continuum QCD within the functional renormalization group [3,4,5] and Dyson-Schwinger equations (DSE) [6,7,8,9,10]
Lattice Monte-Carlo simulations in the formalism of Keldysh path integral are hindered by the notorious ‘sign’ problem, and in order to study observables related to nonperturbative real-time dynamics, e.g., spectral functions in QCD or other strongly correlated system [19, 20], one has to resort to functional continuum methods
In this work we have studied the real-time dynamics of the O(4) scalar theory within the functional renormalization group formulated on the Schwinger-Keldysh closed time path
Summary
The past years have seen rapid progress in our understanding of the strongly correlated physics and its in-medium effects in the context of Euclidean field theories at finite temperature and density, e.g., QCD on a discretized lattice of Euclidean space and time [1, 2], functional continuum QCD within the functional renormalization group (fRG) [3,4,5] and Dyson-Schwinger equations (DSE) [6,7,8,9,10]. One of the relevant pioneer works has been done in [58], where the fRG on a closed time path is employed to study nonthermal fixed points of the O(N ) scalar theory, see [59] Another conceptually different combination between fRG and the Keldysh path integral is put forward in [60,61,62], where the regulation is implemented on the time rather than the renormalization group (RG) scale, such that a time evolution equation for the non-equilibrium effective action is obtained. Note that in Equation (20) we do not include any regulator for the qq-component, since only the real parts of two-point functions are regulated in this work This is adequate for cases in thermal equilibrium, where the Keldysh propagator is related to the retarded and advanced propagators by the fluctuation-dissipation relation as shown in Equation (36) in the following. The Keldysh propagator is essentially composed of the retarded and advanced propagators jointed with an empty circle, which corresponds to iPkK in Equation (38)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
