Related papers: Simplified functional flow equation
The functional renormalization group flow of a scalar field theory with quartic couplings and a sharp spatial momentum cutoff is presented in four-dimensional Minkowski space-time for the bare action by retaining the entanglement of the IR…
We propose a new strategy for the determination of the step scaling function $\sigma(u)$ in finite size scaling studies using the Gradient Flow. In this approach the determination of $\sigma(u)$ is broken in two pieces: a change of the flow…
We propose an exact flow equation for composite operators and their correlation functions. This can be used for a scale-dependent partial bosonization or "flowing bosonization" of fermionic interactions, or for an effective change of…
We introduce Wilson's, or Polchinski's, exact renormalization group, and review the Local Potential Approximation as applied to scalar field theory. Focusing on the Polchinski flow equation, standard methods are investigated, and by…
A continuous sequence of infinitesimal unitary transformations is used to diagonalize the quantum sine-Gordon model for \beta^2\in(2\pi,\infty). This approach can be understood as an extension of perturbative scaling theory since it links…
Governing equations for two-dimensional inviscid free-surface flows with constant vorticity over arbitrary non-uniform bottom profile are presented in exact and compact form using conformal variables. An efficient and very accurate…
We present a strategy for estimating the error of truncated functional flow equations. While the basic functional renormalization group equation is exact, approximated solutions by means of truncations do not only depend on the choice of…
The $\mathcal{O}(\partial^2)$ background independent flow equations for conformally reduced gravity are shown to be equivalent to flow equations naturally adapted to scalar field theory with a wrong sign kinetic term. This sign change is…
In this paper we derive a hierarchy of integral equations from the 4PI effective action which have the form of Bethe-Salpeter equations. We show that the vertex functions defined by these equations can be used to truncate the exact…
We develop a formalism to describe the formation of bound states in quantum field theory using an exact renormalization group flow equation. As a concrete example we investigate a nonrelativistic field theory with instantaneous interaction…
The choice of approximate posterior distribution is one of the core problems in variational inference. Most applications of variational inference employ simple families of posterior approximations in order to allow for efficient inference,…
The flow-equation method of continuous unitary transformations is used to eliminate the minimal quark-gluon interaction in the light-front quantized QCD Hamiltonian. The coupled differential equations in the two lowest Fock sectors…
Motivated by applications in conditional sampling, given a probability measure $\mu$ and a diffeomorphism $\phi$, we consider the problem of simultaneously approximating $\phi$ and the pushforward $\phi_{\#}\mu$ by means of the flow of a…
Emerging sampling algorithms based on normalizing flows have the potential to solve ergodicity problems in lattice calculations. Furthermore, it has been noted that flows can be used to compute thermodynamic quantities which are difficult…
We propose a systematic training-free method to transform the probability flow of a "linear" stochastic process characterized by the equation X_{t}=a_{t}X_{0}+\sigma_{t}X_{1} into a straight constant-speed (SC) flow, reminiscent of…
We study the perturbative behavior of the gradient flow in a twisted box. We apply this information to define a running coupling using the energy density of the flow field. We study the step-scaling function and the size of cutoff effects…
We describe the cosmological dynamics of perfect fluids within the framework of effective field theories. The effective action is a derivative expansion whose terms are selected by the symmetry requirements on the relevant long-distance…
This paper investigates the connections between rectified flows, flow matching, and optimal transport. Flow matching is a recent approach to learning generative models by estimating velocity fields that guide transformations from a source…
We discuss structural aspects of the functional renormalisation group. Flows for a general class of correlation functions are derived, and it is shown how symmetry relations of the underlying theory are lifted to the regularised theory. A…
The scaling properties of quantum gravity are discussed by employing a class of proper-time regulators in the functional flow equation for the conformal factor within the formalism of the background field method. Renormalization group…