相关论文: Beyond Complex Langevin Equations: positive repres…
We study the problem of constructing positive representations of complex measures. In this paper we consider complex densities on a direct product of $U(1)$ groups and look for representations by probability distributions on the…
Complex weights appear in Physics which are beyond a straightforward importance sampling treatment, as required in Monte Carlo calculations. This is the well-known sign problem. The complex Langevin approach amounts to effectively construct…
It is an old idea to replace averages of observables with respect to a complex weight by expectation values with respect to a genuine probability measure on complexified space. This is precisely what one would like to get from complex…
A simple integral relation between a complex weight and the corresponding positive distribution is derived by introducing a second complex variable. Together with the positivity and normalizability conditions, this sum rule allows to…
By introducing a second complex variable, the integral relation between a complex density and the corresponding positive distribution is derived. Together with the positivity and normalizability conditions, this sum rule allows to construct…
Recently found positive representation for an arbitrary complex, gaussian weight is used to construct a statistical formulation of gaussian path integrals directly in the Minkowski time. The positivity of Minkowski weights is achieved by…
The problem of finding a positive distribution, which corresponds to a given complex density, is studied. By the requirement that the moments of the positive distribution and of the complex density are equal, one can reduce the problem to…
After a short review of one of proposals to avoid complex stochastic processes in Complex Langevin studies, the recent progress in the former is reported. In particular, the new developments allow now to construct positive and normalizable…
The problem of effective equations is reviewed and discussed. Starting from the classical Langevin equation, we show how it can be generalized to Hamiltonian systems with non-standard kinetic terms. A numerical method for inferring…
The complex Langevin approach is a promising method for the numerical treatment of systems with a sign problem, for which conventional lattice field theory techniques based on importance sampling cannot be applied. However, complex Langevin…
Complex moment sequences are exactly those which admit positive definite extensions on the integer lattice points of the upper diagonal half-plane. Here we prove that the aforesaid extension is unique provided the complex moment sequence is…
A normalizable complex distribution $P(x)$ on a manifold $\mathcal{M}$ can be regarded as a complex weight, thereby allowing to define expectation values of observables $A(x)$ defined on $\mathcal{M}$. Straightforward importance sampling,…
A simple condition is given that is sufficient to determine whether a measure that is absolutely continuous with respect to a Gau{\ss}ian measure on the space of distributions is reflection positive. It readily generalises conventional…
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…
We derive a family of correctness conditions for complex Langevin simulations. In particular, we show that if in a given theory the expectation values of all observables within a particular space satisfy the theory's Schwinger-Dyson…
One of the yet unsolved questions of QCD in the context of the Standard Model is to explain the strong CP problem. A way to look for a better understanding of it is to investigate the theory in the presence of a non-zero topological theta…
In the landscape of approaches toward the simulation of Lattice Models with complex action the Complex Langevin (CL) appears as a straightforward method with a simple, well defined setup. Its applicability, however, is controlled by certain…
The complex Langevin method is one hopeful candidate to tackle the sign problem. This method is applicable not only to QCD but also to nonrelativistic field theory, such as condensed matter physics. We present the simulation results of a…
The necessity of computing integrals with complex weights over manifolds with a large number of dimensions, e.g., in some field theoretical settings, poses a problem for the use of Monte Carlo techniques. Here it is shown that very general…
We analyze to what extent the complex Langevin method, which is in principle capable of solving the so-called sign problems, can be considered as reliable. We give a formal derivation of the correctness and then point out various…