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The normalization of the quantum corrected action is resolving the equation divergent dependence of the cutoff towards the system apparent result in quantum gravity. Here we consider the normalization to Einstein R twice scalar action with…
The multiplicative and the functional renormalization group methods are applied for the four dimensional scalar theory in Minkowski space-time. It is argued that the appropriate choice of the subtraction point is more important in Minkowski…
We develop the idea that renormalization, decoupling of heavy particle effects from low energy physics and the construction of effective field theories are intimately linked to the momentum space entanglement of disparate modes of an…
We explain how to tropicalize scalar quantum field theory and show that tropicalized massive scalar quantum field theory is exactly solvable. This exact solution manifests as a non-linear recursion equation fulfilled by the expansion…
We present a new method for renormalisation group improvement of the effective potential of a quantum field theory with an arbitrary number of scalar fields. The method amounts to solving the renormalisation group equation for the effective…
After a brief presentation of the exact renormalization group equation, we illustrate how the field theoretical (perturbative) approach to critical phenomena takes place in the more general Wilson (nonperturbative) approach. Notions such as…
We study the exact renormalization group (RG) in $R^2$-gravity in the effective average action formalism using the background field method. The truncated evolution equation (where truncation is made to low-derivatives functionals space) for…
We discuss the Polyakov effective action for a minimally coupled scalar field on a two dimensional curved space by considering a non-local covariant truncation of the effective average action. We derive the flow equation for the form factor…
We analyse approximate solutions to an exact renormalisation group equation with particular emphasis on their dependence on the regularisation scheme, which is kept arbitrary. Physical quantities related to the coarse-grained potential of…
In this work we use the framework of effective field theory to couple Einstein's gravity to scalar electrodynamics and determine the renormalization of the model through the study of physical processes below Planck scale, a realm where…
Real-Space renormalization group techniques are developed for tackling large curvature fluctuations in quantum gravity. Within cells of invariant volume $a^4$, only certain types of fluctuations are allowed. Normal coordinates are used to…
The renormalization-group improved effective potential ---to leading-log and in the linear curvature approximation--- is constructed for ``finite'' theories in curved spacetime. It is not trivial and displays a quite interesting,…
The paper studies a regularization of the quantum (effective) action for a scalar field theory in a general position on a compact smooth Riemannian manifold. As the main method, we propose the use of a special averaging operator, which…
The exact renormalization group is used to study the RG flow of quantities in field theories. The basic idea is to write an evolution operator for the flow and evaluate it in perturbation theory. This is easier than directly solving the…
The perturbative evaluation of the effective action can be expanded in powers of derivatives of the external field. We apply the renormalization group equation to the term in the effective action that is second order in the derivatives of…
The group theoretical quantization scheme is reconsidered by means of elementary systems. Already the quantization of a particle on a circle shows that the standard procedure has to be supplemented by an additional condition on the…
We consider a quantum scalar field with {\lambda}{\phi}^4 interaction in curved spacetimes. The quantum effects are taken into account nonperturbatively using the Hartree approximation to the 2PI effective action. Although this…
We introduce a new framework to analyze quantum algorithms with the renormalization group (RG). To this end, we present a detailed analysis of the real-space RG for discrete-time quantum walks on fractal networks and show how deep insights…
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…
Low-energy effective theories have been used very successfully to study the low-energy limit of QCD, providing us with results for a plethora of phenomena, ranging from bound-state formation to phase transitions in QCD. These theories are…