Related papers: Mean field flow equations and asymptotically free …
We show how to compute real space renormalization group flows in lattice field theory by a self-consistent method. In each step, the integration over the fluctuation field (high frequency components of the field) is performed by a saddle…
We study the response of generating functionals to a variation of parameters (couplings) in equilibrium systems i.e. in quantum field theory (QFT) and equilibrium statistical mechanics. These parameters can be either physical ones such as…
We show how to renormalize Phi-derivable approximations in a theory with a fermionic field coupled to a self-interacting scalar field through a Yukawa interaction. The nonperturbative renormalization concerns the self-interaction coupling…
The problem of renormalization of the semiclassical one-loop equations used in the non-equilibrium field theory is considered. Recently, the renormalizability of such equations has been justified for some special cases of classical field…
Field theoretical renormalization group methods are applied to a simple model of a passive scalar quantity advected by the Gaussian non-solenoidal (``compressible'') velocity field with the covariance $\propto\delta(t-t')|…
For arbitrary four-dimensional quantum field theories with scalars and fermions, renormalisation group equations in the $\overline{\text{MS}}$ scheme are investigated at three-loop order in perturbation theory. Collecting literature…
The gradient flow in non-abelian gauge theories on R^4 is defined by a local diffusion equation that evolves the gauge field as a function of the flow time in a gauge-covariant manner. Similarly to the case of the Langevin equation, the…
Two very different problems that can be studied by renormalization group methods are discussed with the aim of showing the conceptual unity that renormalization group has introduced in some areas of theoretical Physics. The two problems…
The phase transition to superfluidity and the BCS-BEC crossover for an ultracold gas of fermionic atoms is discussed within a functional renormalization group approach. Non-perturbative flow equations, based on an exact renormalization…
Scale separation is an important physical principle that has previously enabled algorithmic advances such as multigrid solvers. Previous work on normalizing flows has been able to utilize scale separation in the context of scalar field…
Numerous correlated electron systems exhibit a strongly scale-dependent behavior. Upon lowering the energy scale, collective phenomena, bound states, and new effective degrees of freedom emerge. Typical examples include (i) competing…
Looking for an observable manifestation of the so-called unnaturalness of scalar fields we introduce a seemingly new set of differential equations for connected Green functions. These equations describe the momentum dependence of the Green…
Two-loop renormalization group equations in gauge theories with multiple U(1) groups are presented. Instead of normalizing the abelian gauge fields in canonical forms, we retain kinetic-mixing terms and treat the mixing coefficients as free…
The quantum field theory of two-dimensional sigma models with bulk and boundary couplings provides a natural framework to realize and unite different species of geometric flows that are of current interest in mathematics. In particular, the…
I present a sequence of non-perturbative approximate solutions for scalar $\phi^4$ theory for arbitrary interaction strength, which contains, but allows to systematically improve on, the familiar mean-field approximation. This sequence of…
We review the gradient flow for gauge and fermion fields and its applications to lattice gauge theory computations. Using specific examples, we discuss the interplay between perturbative and non-perturbative calculations in the context of…
Working with scalar field theories, we discuss choices of regulator that, inserted in the functional renormalization group equation, reproduce the results of dimensional regularization at one and two loops. The resulting flow equations can…
We investigate fermionic quantum field theories using functional renormalisation. In the limit of many fermion flavours $N$, we demonstrate that theories have exact solutions for their quantum effective actions given by quasi-local…
We propose a generalization of the gradient flow equation for quantum field theories with nonlinearly realized symmetry. Applying the equation to $\mathcal{N}=1$ $SU(N)$ super Yang-Mills theory in four dimensions, we construct a…
We adapt the precise definition of the flowing effective action in order to obtain a functional flow equation with simple properties close to physical intuition. The simplified flow equation is invariant under local gauge transformations…