Related papers: Renormdynamics and Generalized Analytic Functions
We present here analytic expressions for the generalised Lindhard function, also referred to as Fermi Gas polarisation propagator, in a relativistic kinematic framework and in the presence of various resonances and vertices. Particular…
Novel analytic solutions are derived for integrals that involve the generalized Marcum Q-function, exponential functions and arbitrary powers. Simple closed-form expressions are also derived for the specific cases of the generic integrals.…
The purpose of this publication is to derive and discuss equations of motion of affinely rigid (homogeneously deformable) body moving in Euclidean space of general dimension $n$. Our aim is to present some analytical methods and to discuss…
A Generalized Kinetic Theory was proposed in order to have the possibility to treat particles which obey a very general statistics. By adopting the same approach, we generalize here the Kinetic Theory of electrons and phonons. Equilibrium…
Canonical functions are a powerful concept with numerous applications in the study of groups, monoids, and clones on countable structures with Ramsey-type properties. In this short note, we present a proof of the existence of canonical…
We derive renormalised finite functional flow equations for quantum field theories in real and imaginary time that incorporate scale transformations of the renormalisation conditions, hence implementing a flowing renormalisation. The flows…
An elementary system leading to the notions of fractional integrals and derivatives is considered. Various physical situations whose description is associated with fractional differential equations of motion are discussed.
A generalized canonical form of multi-time dynamical theories is proposed. This form is a starting point for a modified canonical quantization procedure of theories based on a quantum version of the action principle. As an example, the…
In view of the usefulness and importance of the kinetic equation in certain physical problems, the authors derive the explicit solution of a fractional kinetic equation of general character, that unifies and extends earlier results.…
In this short, conceptual paper we observe that essentially the same mathematics applies in three contexts with disparate literatures: (1) sigmoidal and RBF approximation of smooth functions, (2) rational approximation of analytic functions…
The basics of RG equations for generic partition functions are briefly reviewed, keeping in mind an application to the Polyakov-de Boer-Verlindes description of the holomorphic RG flow.
In view of the role of reaction equations in physical problems, the authors derive the explicit solution of a fractional reaction equation of general character, that unifies and extends earlier results. Further, an alternative shorter…
The aim of this paper is to define a new operator by using the generalized Struve functions. By using this operator we define a subclass of analytic functions. We discuss some properties of this class such as inclusion problems, radius…
Functional conjugation methods are used to analyze the global structure of various renormalization group trajectories, and to gain insight into the interplay between continuous and discrete rescaling. With minimal assumptions, the methods…
Critical analyses of well-known methods of derivation of kinetic and hydrodynamic equations is presented. Another method of derivation of kinetic and hydrodynamic equations from classic mechanics is described. It is shown that equations of…
We present a formalism that represents pure states, mixtures and generalized states as functionals on an algebra containing the observables of the system. Along these states, there are other functionals that decay exponentially at all times…
One-parameter generalizations of the logarithmic and exponential functions have been obtained as well as algebraic operators to retrieve extensivity. Analytical expressions for the successive applications of the sum or product operators on…
Generalized trigonometric functions (GTFs) are simple generalization of the classical trigonometric functions. GTFs are deeply related to the $p$-Laplacian, which is known as a typical nonlinear differential operator. Compared to GTFs with…
We discuss recent developments in the study of quantum wavefunctions and transport in classically ergodic systems. Surprisingly, short-time classical dynamics leaves permanent imprints on long-time and stationary quantum behavior, which are…
We discuss a method to analytically continue functional renormalization group equations from imaginary Matsubara frequencies to the real frequency axis. In this formalism, we investigate the analytic structure of the flowing action and the…