Related papers: S-Matrix Elements in General Renormalization Schem…
We use the Schwinger-Dyson equations as a starting point to derive renormalization flow equations. We show that Katanin's scheme arises as a simple truncation of these equations. We then give the full renormalization group equations up to…
The present lectures are a practical guide to the calculation of radiative corrections to the Green functions in quantum field theory. The appearance of ultraviolet divergences is explained, their classification is given, the…
We propose and investigate a large class of models possessing resonance factorized S-matrices. The associated Casimir energy describes a rich pattern of renormalization group trajectories related to flows in the coset models based on the…
We discuss the concepts and the framework of the renormalization procedure in regularization-invariant momentum subtraction schemes. These schemes are used in the context of lattice simulations for the determination of physical quantities…
Harder's reduction theory provides filtrations of euclidean buildings that allow one to deduce cohomological and homological properties of S-arithmetic groups over global function fields. In this survey I will sketch the main points of…
The renormalization equations emerge from a Greenian-matrix solution of the discretized Schrodinger equation. A by-product of these equations is the decimation process, which enables substituted-benzenes to be mapped onto corresponding…
This paper investigates the reconstruction of elastic Green's function from the cross-correlation of waves excited by random noise in the context of scattering theory. Using a general operator equation, -the resolvent formula-, Green's…
We study the $S$-matrix of Goldstones in the renormalizable theory of a $U(1)$ complex scalar at finite charge, i.e. in a state that breaks Lorentz invariance. The theory is weakly coupled so that this $S$-matrix exists at all energies.…
The generalized minimal subtraction scheme for ultraviolet renormalization (Kuznetsov and Tkachov, 1988) is fine-tuned with applications in mind. The resulting $\text{MS}^4$ scheme obviates extraneous regularizations and renders momentum…
The renormalization group equations for the general 2 by 2, complex, neutrino mass matrix are shown to have exact, analytic solutions. Simple formulas are given for the physical mixing angle, complex phase and mass ratio in terms of their…
We present an explicit numerical method to obtain the Cartan-Khaneja-Glaser decomposition of a general element G of SU(2^N) in terms of its `Cartan' and `non-Cartan' components. This effectively factors G in terms of group elements that…
Under renormalization, physical operators can mix with operators which vanish by the equations of motion. Such operators cannot contribute to matrix elements between physical states, but they contribute to operator mixing in renormalization…
The non-renormalization theorems of chiral vertex functions are derived on the basis of an algebraic analysis. The property, that the interaction vertex is a second supersymmetry variation of a lower dimensional field monomial, is used to…
The Stueckelberg-Petermann renormalization group is the group of finite renormalizations of the S-matrix in the framework of causal perturbation theory. The renormalization group in the sense of Wilson relies usually on a functional…
We derive a multiplication law for free non-hermitian random matrices allowing for an easy reconstruction of the two-dimensional eigenvalue distribution of the product ensemble from the characteristics of the individual ensembles. We define…
The perturbative construction of the S-matrix in the causal spacetime approach of Epstein and Glaser may be interpreted as a method of regularization for divergent Feynman diagrams. The results of any method of regularization must be…
The S-matrix in the static limit of a dispersion relation has a finite order N and is a matrix of meromorfic functions of energy in the complex plane with cuts. In the elastic case it reduces to N functions connected by the crossing…
In this paper, we propose a Green's basis and also a new physical basis for dimension-seven (dim-7) operators, which are suitable for the matching of ultraviolet models onto the Standard Model effective field theory (SMEFT) and the…
In our article we consider some algebraical methods which may be useful in some inverse spectral problems. The reconstraction of the matrix from its minors is considered.
In terms of a rephasing invariant parametrization, the set of renormalization group equations (RGE) for Dirac neutrino parameters can be cast in a compact and simple form. These equations exhibit manifest symmetry under flavor permutations.…