Related papers: On the importance of the normalization
For a number field $K$, we extend the notion of the ring class field of an order in $K$ [C. Lv and Y. Deng, SciChina. Math., 2015] to that of an arbitrary number ring in $K$. We give both ideal-theoretic and idele-theoretic description of…
A regularization for effective field theory with two propagating heavy particles is constructed. This regularization preserves the low-energy analytic structure, implements a low-energy power counting for the one-loop diagrams, and…
These lectures illustrate the key ideas of modern renormalization theory and effective field theories in the context of simple nonrelativistic quantum mechanics and the Schr\"odinger equation. They also discuss problems in QED, QCD and…
We study the pull-back of regular 1-forms on a complex irreducible plane curve singularity under the normalization morphism.
The "Krein" regularization method of quantum field theory is studied, inspired by the Krein space quantization and quantum metric fluctuations. It was previously considered in the one-loop approximation, and this paper is generalized to all…
As a continuation of previous investigations, the formalism used there is extended to the case when an external electric field is present and the covariant formulation is performed again. The equation system obtained allows no restriction…
The choice of the regularization scheme in Loop Quantum Cosmology (LQC) is crucial for the predicted phenomenology. We outline how the improved scheme can be naturally realized in Quantum Reduced Loop Gravity, describing the Universe as an…
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…
Rules of quantization and equations of motion for a finite-dimensional formulation of Quantum Field Theory are proposed which fulfill the following properties: a) both the rules of quantization and the equations of motion are covariant; b)…
We give an introduction to renormalisation, focusing first on a pedagogical description of fundamental concepts of the procedure and its features, then we introduce the renormalisation group and its equations. We discuss then the case of…
We present a simple derivation of the Lamb shift using effective field theory techniques and dimensional regularisation.
The method recently proposed by Skala and Cizek for calculating perturbation energies in a strict sense is ambiguous because it is expressed as a ratio of two quantities which are separately divergent. Even though this ratio comes out…
The usual proof of renormalizability using the Callan-Symanzik equation makes explicit use of normalization conditions. It is shown that demanding that the renormalization group functions take the form required for minimal subtraction…
We study Dirac field equations coupled to electrodynamics with metric and torsion fields: we discuss how special spinorial solutions are incompatible with torsion; eventually these results will be used to sketch a discussion on the problem…
We revise the problem of the quantization of relativistic particle models (spinless and spinning), presenting a modified consistent canonical scheme. One of the main point of the modification is related to a principally new realization of…
This work is a natural continuation of our recent study in quantizing relativistic particles. There it was demonstrated that, by applying a consistent quantization scheme to a classical model of a spinless relativistic particle as well as…
We consider a possibility to unify the methods of regularization, such as the renormalization group method, stochastic quantization etc., by the extension of the standard field theory of the square-integrable functions $\phi(b)\in…
In this article we prove spin statistics theorem for arbitrary massive (A, B) field in a representation theoretic manner. General Gamma matrices are introduced, and explicit forms for low spin are calculated. Spin sums and twisted spin sums…
We discuss some formal aspects of quantum anomalies with an emphasis on the regularization of field theory. We briefly review how ambiguities in perturbation theory have been resolved by various regularization schemes. To single out the…
The summation of logarithmic contributions to perturbative radiative corrections in physical processes through use of the renormalization group equation has proved to be a useful way of enhancing the information one can obtain from explicit…