Related papers: Exact Renormalisation Group Equations and Loop Equ…
A proper formulation in the perturbative renormalization group method is presented to deduce amplitude equations. The formulation makes it possible not only avoiding a serious difficulty in the previous reduction to amplitude equations by…
This paper is a self contained review of the Loop Variable approach to string theory. The Exact Renormalization Group is applied to a world sheet theory describing string propagation in a general background involving both massless and…
We study exact renormalization group equations in the framework of the effective average action. We present analytical approximate solutions for the scale dependence of the potential in a variety of models. These solutions display a rich…
We incorporate running parameters and anomalous dimensions into the framework of the exact renormalization group. We modify the exact renormalization group differential equations for a real scalar field theory, using the anomalous…
We show that the Tensor Renormalization Group (TRG) method can be applied to O(N) spin models, principal chiral models and pure gauge theories (Z2, U(1) and SU(2)) on (hyper) cubic lattices. We explain that contrarily to some common belief,…
The exact renormalization group is applied to a nonlinear diffusion equation with a discontinuous diffusion coefficient. The generating functional of the solution for the initial-value problem of nonlinear diffusion equations is first…
The renormalization of higher-dimensional operators in quantum field theory is essential for phenomenological analyses in particle physics, and plays a significant role in the study of critical phenomena. We present a framework for…
A proper version of the proto renormalization-group scheme is presented to derive amplitude equations in striped pattern formation with conserved and nonconserved order parameter. In the conserved case, the result preserves the conservation…
Exact Renormalization Group techniques are applied to supersymmetric models in order to get some insights into the low energy effective actions of such theories. Starting from the ultra-violet finite mass deformed N=4 supersymmetric…
Using the example of the two-dimensional (2D) Ising model, we show that in contrast to what can be done in configuration space, the tensor renormalization group (TRG) formulation allows one to write exact, compact, and manifestly local…
We discuss the reformulation of the O(2) model with a chemical potential and the Abelian Higgs model on a 1+1 dimensional space-time lattice using the Tensor Renormalization Group (TRG) method. The TRG allows exact blocking and connects…
We overview the entire renormalization theory, both perturbative and non-perturbative, by the method of the exact renormalization group (ERG). We emphasize particularly on the perturbative application of the ERG to the phi4 theory and QED…
We study the $SU(2)$ gauge-Higgs model in two Euclidean dimensions using the tensor renormalization group (TRG) approach. We derive a tensor formulation for this model in the unitary gauge and compare the expectation values of different…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
The results of the renormalization group are commonly advertised as the existence of power law singularities near critical points. The classic predictions are often violated and logarithmic and exponential corrections are treated on a…
The exact renormalization group (ERG) is formulated implementing the decimation of degrees of freedom by means of a particular momentum integration measure. The definition of this measure involves a distribution that links this decimation…
We discuss the formulation of "thermal renormalization group-equations" and their application to the finite temperature phase-transition of scalar O(N)-theories. Thermal renormalization group-equations allow for a computation of both the…
Within the framework of the functional renormalization group, we derived the flow equations for the scale-dependent effective action at finite temperature for models involving an antisymmetric rank-2 tensor field. The analysis focuses on…
We discuss exact renormalization group (RG) in $R^2$-gravity using effective average action formalism. The truncated evolution equation for such a theory on De Sitter background leads to the system of nonperturbative RG equations for…
For arbitrary scalar QFTs in four dimensions, renormalisation group equations of quartic and cubic interactions, mass terms, as well as field anomalous dimensions are computed at three-loop order in the $\overline{\text{MS}}$ scheme.…