Related papers: How to Renormalize the Schrodinger Equation
These introductory notes are about functional renormalization group equations and some of their applications. It is emphasised that the applicability of this method extends well beyond critical systems, it actually provides us a general…
This is a further explanation of a new and simple renormalization approach recently proposed by the author (hep-th/9708104, Ref. [1], that is somewhat sketchy) for any ordinary QFT (whether renormalizable or not) in any spacetime dimension.…
We derive the renormalization group equations for a generic nonrenormalizable theory. We show that the equations allow one to derive the structure of the leading divergences at any loop order in terms of one-loop diagrams only. In chiral…
The structure of the renormalization group equations for the low energy effective theory of gravity coupled to a scalar field is presented. An approximate solution to these equations with a finite number of independent renormalized…
An exact renormalization group for theories of a scalar chiral superfield is formulated, directly in four dimensional Euclidean space. By constructing a projector which isolates the superpotential from the full Wilsonian effective action,…
In this work we present the study of the renormalizability of the Generalized Quantum Electrodynamics ($GQED_{4}$). We begin the article by reviewing the on-shell renormalization scheme applied to $GQED_{4}$. Thereafter, we calculate the…
This paper studies uniqueness and nonuniqueness for potential reconstruction from one boundary measurement in quantum fields, associated with the steady state Schr\"{o}dinger equation. A uniqueness theorem of the inverse problem is…
Schr\"odinger equation with potential $-g/r^2$ exhibits a limit cycle, described in the literature in a broad range of contexts using various regularizations of the singularity at $r=0$. Instead, we use the renormalization group…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
New solutions to the non perturbative renormalization group equation for the effective action of a scalar field theory in the Local Potential Approximation having the exponential form $e^{\pm\phi}$ are found. This result could be relevant…
This thesis is devoted to studying aspects of real-time nonequilibrium dynamics in quantum field theory by implementing an initial value formulation of quantum field theory. The main focus is on the linear relaxation of mean fields and…
Basic elements of the exact renormalization group method and recent results within this approach are reviewed. Topics covered are the derivation of equations for the effective action and relations between them, derivative expansion,…
We relate renormalization in perturbative quantum field theory to the theory of limiting mixed Hodge structures using parametric representations of Feynman graphs.
In effective field theories, the concept of renormalization of perturbative divergences is replaced by renormalization group concepts such as relevance and universality. Universality is related to cutoff scheme independence in…
This is a lecture note on the renormalization group theory for field theory models based on the dimensional regularization method. We discuss the renormalization group approach to fundamental field theoretic models in low dimensions. We…
The problem of renormalization of the semiclassical one-loop equations used in the non-equilibrium field theory is considered. Recently, the renormalizability of such equations has been justified for some special cases of classical field…
We discuss an alternative method to mass renormalize a quantum field Hamiltonian based on a requirement that the vacuum and single-particle sectors are not self-scattering. We illustrate the feasibility of this method for the concrete…
A modified perturbation theory in the strength of the nonlinear term is used to solve the Nonlinear Schroedinger Equation with a random potential. It is demonstrated that in some cases it is more efficient than other methods. Moreover we…
We study admissible and equivalence point transformations between generalized multidimensional nonlinear Schr\"odinger equations and classify Lie symmetries of such equations. We begin with a wide superclass of Schr\"odinger-type equations,…
After a brief historical review of the emergence of QCD as the quantum field theory of strong interactions, the basic notions of colour and gauge invariance are introduced leading to the QCD Lagrangian. The second lecture is devoted to…