Related papers: BBGKY Hierarchy in Scalar QFT
Krylov subspace methods are a powerful family of iterative solvers for linear systems of equations, which are commonly used for inverse problems due to their intrinsic regularization properties. Moreover, these methods are naturally suited…
We reconstruct the field potentials in case of (non)phantom fields for different models resulting from parametrization of q(t), a(t) or H(t). In addition we carry out similar procedure for tachyonic field. We also discuss specific form of…
Building on arXiv:1911.05827, we uncover new properties of type-B conformal anomalies for Coulomb-branch operators in continuous families of 4D $\mathcal{N}=2$ SCFTs. We study a large class of such anomalies on the Higgs branch, where…
We present a quick introduction to quantum field theory and Wilson's theory of the renormalization group from the point of view of mathematical analysis. The presentation is geared primarily towards a probability theory, harmonic analysis…
In this overview paper a direct approach to q-Chebyshev polynomials and their elementary properties is given. Special emphasis is placed on analogies with the classical case. There are also some connections with q-tangent and q-Genocchi…
We study the coupled equations describing fluctuations of scalars and the metric about background solutions of N=8 gauged supergravity which are dual to boundary field theories with renormalization group flow. For the case of a kink…
We provide a general method for constructing bosonic Bogoliubov transformations that diagonalize a general class of quadratic Hamiltonians. These Hamiltonians describe the pair interaction models. Bogoliubov transformations are constructed…
Renormalization techniques in perturbative quantum field theory were known, from their inception, to have a strong combinatorial content emphasized, among others, by Zimmermann's celebrated forest formula. The present article reports on…
The main result of this paper is the construction of a conformally covariant operator in two dimensions acting on scalar fields and containing fourth order derivatives. In this way it is possible to derive a class of Lagrangians invariant…
The content of this paper is incorporated into hep-th/9805093
In two dimensional constructive quantum field theory for scalar fields, it is necessary to regularize both the action and the total (Gaussian) volume. In this note we consider the compatibility of these regularizations.
Any field, even if it lives in a completely hidden sector, interacts with the visible sector at least via the gravitational interaction. In this paper, we show that a scalar field in such a hidden sector generically couples to the quadratic…
An explicit structure relation for Askey-Wilson polynomials is given. This involves a divided q-difference operator which is skew symmetric with respect to the Askey-Wilson inner product and which sends polynomials of degree n to…
A class of non-linear eigenvalue problems defined in the form of operator polynomials is investigated. The problems are related to wave equations which appear in a relativistic quantum field theory. Spectral asymptotics for this class are…
The Fast Fourier Transform is extended to functions on finite graphs whose edges are identified with intervals of finite length. Spectral and pseudospectral methods are developed to solve a wide variety of time dependent partial…
We develop a systematic approach to the classical Boussinesq (cBsq) hierarchy based on an elementary polynomial recursion formalism. Moreover, the gauge equivalence between the cBsq and AKNS hierarchies is studied in detail and used to…
We consider the fractional generalizations of the phase volume, volume element and Poisson brackets. These generalizations lead us to the fractional analog of the phase space. We consider systems on this fractional phase space and…
We study the non-equilibrium dynamics of a system of coupled scalar fields in a Friedmann-Robertson-Walker (FRW) universe. We consider the evolution of spatially homogeneous "classical" fields and of their quantum fluctuations including the…
The renormalization group evolution of $\Delta B=2$ transition operators is studied at leading order in heavy quark effective theory and at next-to-leading order in QCD. We calculate new contributions that were not taken into account in…
The Quantum Fourier Transformation (QFT) is a well-known subroutine for algorithms on qubit-based universal quantum computers. In this work, the known QFT circuit is used to derive an efficient circuit for the multidimensional QFT. The…