Related papers: Wavelet based regularization for Euclidean field t…
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part we consider application of FWT to metaplectic…
In the present paper, new classes of wavelet functions are presented in the framework of Clifford analysis. Firstly, some classes of orthogonal polynomials are provided based on 2-parameters weight functions. Such classes englobe the well…
Elements of the quantization in field theory based on the covariant polymomentum Hamiltonian formalism (the De Donder-Weyl theory), a possibility of which was originally discussed in 1934 by Born and Weyl, are developed. The approach is…
Wavelet Transforms are a widely used technique for decomposing a signal into coefficient vectors that correspond to distinct frequency/scale bands while retaining time localization. This property enables an adaptive analysis of signals at…
This paper first summarizes the foundations of stochastic calculus via regularization and constructs through this procedure It\^o and Stratonovich integrals. In the second part, a survey and new results are presented in relation with finite…
Effective field theories with (large) extra dimensions are studied within a physical regularization scheme provided by string theory. Explicit string calculations then allow us to consistently analyze the ultraviolet sensitivity of…
Algebraic quantum field theory is an approach to relativistic quantum physics, notably the theory of elementary particles, which complements other modern developments in this field. It is particularly powerful for structural analysis but…
We give a rigorous description of a model of the quantized electromagnetic field interacting with quantized current fields. In the special case of classical currents our results agree with common knowledge about the problem. A toy model of…
Stochastic field equations for linearized gravity are presented. The theory is compared with the usual quantum field theory and questions of Lorentz covariance are discussed. The classical radiation approximation is also presented.
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 describe a new viewpoint on canonical quantization of linear fields on a general curved background that encompasses and generalizes the standard treatment of canonical QFT given in textbooks. Our method permits the construction of pure…
A complete characterization of the structure of nuclei can be obtained by combining information arising from inelastic scattering, Coulomb excitation and $\gamma-$decay, together with one- and two-particle transfer reactions. In this way it…
The Wick rotation provides the standard technique of computing Feynman diagrams by means of Euclidean propagators. Let us suppose that quantum fields in an interaction zone are really Euclidean. In contrast with the well-known Euclidean…
This paper provides explicit and detailed quantum field theory (QFT) computations of polarizations correlations of emerging particles in several processes in QED, Electroweak Theory, and even in particle productions from strings, and hence…
This note introduces a new family of wavelets and a multiresolution analysis, which exploits the relationship between analysing filters and Floquet's solution of Mathieu differential equations. The transfer function of both the detail and…
The underlying mathematics of the wavelet formalism is a representation of the inhomogeneous Lorentz group or the affine group. Within the framework of wavelets, it is possible to define the ``window'' which allows us to introduce a…
We introduce a new regularization technique, using what we refer to as the Steklov regularization function, and apply this technique to devise an algorithm that computes a global minimizer of univariate coercive functions. First, we show…
The asymptotic high momentum behaviour of quantum field theories with cubic interactions is investigated using renormalization group techniques in the asymmetric limit x << 1. Particular emphasis is paid to theories with interactions…
We discuss the formulation of a non-relativistic effective field theory for two-body P-wave scattering in the presence of shallow states and critically address various approaches to renormalization proposed in the literature. It is…
We give formulas for the number of polynomials over a finite field with given root multiplicities, in particular in cases when the formula is surprisingly simple (a power of q). Besides this concrete interpretation, we also prove an…