Related papers: The scaling and mass expansion
This article investigates the averaging of a scalar degree of freedom that couples universally to matter. It quantifies the approximation of smoothing the matter distribution before solving the Klein--Gordon equation. In the case of Yukawa…
The dilation invariance is studied in the framework of Epstein-Glaser approach to renormalization theory. Some analogues of the Callan-Symanzik equations are found and they are applied to the scalar field theory and to Yang-Mills models. We…
A reorganized perturbation expansion with a propagator of soft infrared behavior is used to study the critical behavior of the mass gap. The condition of relativistic covariance fixes the form of the soft propagator. Finite approximants to…
We develop a scaling theory of the unjamming transition of soft frictionless disks in two dimensions by defining local areas, which can be uniquely assigned to each contact. These serve to define local order parameters, whose distribution…
A higher-derivative, interacting, scalar field theory in curved spacetime with the most general action of sigma-model type is studied. The one-loop counterterms of the general theory are found. The renormalization group equations…
In the spirit of classic works of Wilson on the renormalization group and operator product expansion, a new framework for the study of the theory space of euclidean quantum field theories has been introduced. This formalism is particularly…
The free energy of the Coulomb Gap problem is expanded as a set of Feynman diagrams, using the standard diagrammatic methods of perturbation theory. The gap in the one-particle density of states due to long-ranged interactions corresponds…
An alternative perturbative expansion in quantum mechanics which allows a full expression of the scaling arbitrariness is introduced. This expansion is examined in the case of the anharmonic oscillator and is conveniently resummed using a…
Certain power-counting non-renormalizable theories, including the most general self-interacting scalar fields in four and three dimensions and fermions in two dimensions, have a simplified renormalization structure. For example, in…
A modification of perturbation theory, known as delta-expansion (variationally improved perturbation), gave rigorously convergent series in some D=1 models (oscillator energy levels) with factorially divergent ordinary perturbative…
A recently developed variational resummation technique, incorporating renormalization group properties consistently, has been shown to solve the scale dependence problem that plagues the evaluation of thermodynamical quantities, e.g.,…
McMillan and Mayer (MM) proved two remarkable theorems in their paper on the equilibrium statistical mechanics of liquid solutions. They first showed that the grand canonical partition function for a solution can be reduced to a one with an…
We illustrate the importance of mass scales and their relation in the specific case of the linear sigma model within the context of its one loop Ward identities. In the calculation it becomes apparent the delicate and essential connection…
In this work, we discuss how the linear and non-linear advection terms modify the scaling behavior of the continuous symmetry breaking and stabilize the long-range order, even in $d=2$ far from equilibrium, by means of simple scaling…
We show how the exact renormalization group for the effective action with a sharp momentum cutoff, may be organised by expanding one-particle irreducible parts in terms of homogeneous functions of momenta of integer degree (Taylor…
This work is devoted to the study of the scaling, and the consequent power-law behavior, of the correlation function in a mutation-replication model known as the expansion-modification system. The latter is a biology inspired random…
In real-world applications, observations are often constrained to a small fraction of a system. Such spatial subsampling can be caused by the inaccessibility or the sheer size of the system, and cannot be overcome by longer sampling.…
We demonstrate that in the mass independent renormalization scheme. the renormalization group equations associated with the unphysical parameters that characterize the renormalization scheme and the mass scale leads to summation that…
The concept of scaling algebra provides a novel framework for the general structural analysis and classification of the short distance properties of algebras of local observables in relativistic quantum field theory. In the present article…
The renormalization method is specifically aimed at connecting theories describing physical processes at different length scales and thereby connecting different theories in the physical sciences. The renormalization method used today is…