Related papers: Geometrical Renormalization Groups: Perfect Decons…
Hierarchical renormalization group transformations are related to non-associative algebras. Non-trivial infrared fixed points are shown to be solutions of polynomial equations. At the example of a scalar model in $d(\ge2)$ dimensions some…
The necessity of renormalization arises from the infinite integrals which are caused by the discrepancy between the orders of differential and integral operators in the four dimensional QFTs. Therefore in view of the fact that finiteness…
Nonperturbative approximation schemes based on two-particle irreducible (2PI) effective actions provide an important means for our current understanding of (non-)equilibrium quantum field theory. A remarkable property is their…
For actions with a dense orbit of a connected noncompact simple Lie group $G$, we obtain some global rigidity results when the actions preserve certain geometric structures. In particular, we prove that for a $G$-action to be equivalent to…
A field theoretic renormalization group method is presented which is capable of dealing with crossover problems associated with a change in the upper critical dimension. The method leads to flow functions for the parameters and coupling…
The Wilsonian exact renormalization group gives a natural framework in which ultraviolet and infrared divergences can be treated separately. In massless QED we introduce, as the only mass parameter, a renormalization scale $\L_R > 0$. We…
A totally symmetric set is a finite subset of a group for which any permutation of the elements can be realized by conjugation in the ambient group. Such sets are rigid under homomorphisms, and so exert a great deal of control over the…
We compute the influence action for a system perturbatively coupled to a linear scalar field acting as the environment. Subtleties related to divergences that appear when summing over all the modes are made explicit and clarified. Being…
We formulate a quantization commutes with reduction principle in the setting where the Lie group $G$, the symplectic manifold it acts on, and the orbit space of the action may all be noncompact. It is assumed that the action is proper, and…
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…
Let $G$ be a noncompact real algebraic group and $\G<G$ a lattice. One purpose of this paper is to show that there is an smooth, volume preserving, mixing action of $G$ or $\G$ on a compact manifold which admits a smooth deformation. We…
In this article we study the normal bundle and the deformation to the normal cone functors to get deformation Lie groupoids that allow us to construct pushforward maps in any suitable (co)homology theory for Lie groupoids (not only…
Discrete amorphous materials are best described in terms of arbitrary networks which can be embedded in three dimensional space. Investigating the thermodynamic equilibrium as well as non-equilibrium behavior of such materials around second…
The effective action in quantum general relativity is strongly dependent on the gauge-fixing and parametrization of the quantum metric. As a consequence, in the effective approach to quantum gravity, there is no possibility to introduce the…
In this paper, we revisit scalar field theories in $d$ space-time dimensions possessing $U(N)$ global symmetry. Following our recent work arXiv:1402.1430v2, we consider the generating function of correlation functions of all…
We revisit here the problem of generalized cosmology using renormalization group approach. A complete analysis of these cosmologies, where specific models appear as asymptotic fixed-points, is given here along with their linearized…
Let $G$ be a linear connected non-compact real simple Lie group and let $K\subset G$ be a maximal compact subgroup of $G$. Suppose that the centre of $K$ isomorphic to $\mathbb{S}^1$ so that $G/K$ is a global Hermitian symmetric space. Let…
We provide a non-technical overview of recent extensions of renormalization methods and techniques to Group Field Theories (GFTs), a class of combinatorially non-local quantum field theories which generalize matrix models to dimension $d…
Starting from a local quantum field theory with an unbroken compact symmetry group $G$ in 1+1-dimensional spacetime we construct disorder fields implementing gauge transformations on the fields (order variables) localized in a wedge region.…
The renormalization group is the cornerstone of the modern theory of universality and phase transitions, a powerful tool to scrutinize symmetries and organizational scales in dynamical systems. However, its network counterpart is…