Related papers: Complex Langevin Equations and Schwinger-Dyson Equ…
The path integral by which quantum field theories are defined is a particular solution of a set of functional differential equations arising from the Schwinger action principle. In fact these equations have a multitude of additional…
Complex Langevin simulations provide an alternative to sample path integrals with complex weights and therefore are suited to determine the phase diagram of QCD from first principles. Adaptive step-size scaling and gauge cooling are used to…
Self-interacting scalar quantum field theories possessing $PT$-symmetry are physically admissible since their energy spectrum is real and bounded below. However, models with $PT$-invariant potentials can have complex actions in general and…
Complex Langevin simulations provide an alternative to sample path integrals with complex weights and therefore are suited to determine the phase diagram of QCD from first principles. We use our proposed method of Dynamic Stabilisation (DS)…
Different quantum Langevin equations obtained by coupling a particle to a field are examined. Instabilities or violations of causality affect the motion of a point charge linearly coupled to the electromagnetic field. In contrast, coupling…
Quantum field theories and Matrix models have a far richer solution set than is normally considered, due to the many boundary conditions which must be set to specify a solution of the Schwinger-Dyson equations. The complete set of solutions…
Lattice field theories with a complex action can be studied numerically by allowing a complexified configuration space to be explored. Here we compare the recently introduced formulation on a Lefschetz thimble with the result from…
We construct an effective potential for the complex Langevin equation on a lattice. We show that the minimum of this effective potential gives the space-time and Langevin time average of the complex Langevin field. The loop expansion of the…
We derive quantum Boltzmann equations from Schwinger-Dyson equations in gradient expansion for a weakly coupled scalar field theory with a spatially varying mass. We find that at higher order in gradients a full description of the system…
Stochastic quantization offers the opportunity to simulate field theories with a complex action. In some theories unstable trajectories are prevalent when a constant stepsize is employed. We construct algorithms for generating an adaptive…
Complex Langevin dynamics can be used to perform numerical simulations of theories with a complex action. In order to justify the procedure, it is important to understand the properties of the real and positive distribution, which is…
Non-perturbative formulations of field theories are essential to capture intriguing physical phenomena, including confinement in QCD, spontaneous supersymmetry breaking, and dynamical compactification in superstrings. Lattice regularization…
Given any (Feynman) propagator which is Lorentz and translation invariant, it is possible to construct an action functional for a scalar field such that the quantum field theory, obtained by path integral quantization, leads to this…
This chapter [of a supplement to Prog. Theo. Phys.] reviews numerical simulations of quantum field theories based on stochastic quantization and the Langevin equation. The topics discussed include renormalization of finite step-size…
In this review we present the current state-of-the-art on complex Langevin simulations and their implications for the QCD phase diagram. After a short summary of the complex Langevin method, we present and discuss recent developments. Here…
Real time evolution of a scalar field theory is investigated. The severe sign problem is circumvented using the Complex Langevin equation. The naive application of the method breaks down for extended real times due to the appearance of…
Simulations of QCD with a finite chemical potential typically lead to a severe sign problem, prohibiting any standard Monte Carlo approach. Complex Langevin simulations provide an alternative to sample path integrals with oscillating weight…
The Feynman Path Integral is extended in order to capture all solutions of a quantum field theory. This is done via a choice of appropriate integration cycles, parametrized by M in SL(2,C), i.e., the space of allowed integration cycles is…
We consider a general solution of the Langevin equation describing massive fermions to an appropriate boundary problem. Assuming existence of such solution we show that its correlators coincide with the Schwinger functions of corresponding…
Nonlinear, multiplicative Langevin equations for a complete set of slow variables in equilibrium systems are generally derived on the basis of the separation of time scales. The form of the equations is universal and equivalent to that…