Related papers: Perturbative S-matrices with non-provisional regul…
In the context of non-relativistic quantum field theory, a method is proposed for multiplying field operators at the same spatial point and obtaining regular (i.e. rigorously defined) interaction terms for the Hamiltonian. The basic idea is…
The analytic structure of the S-matrix of singular quantum mechanics is examined within a multichannel framework, with primary focus on its dependence with respect to a parameter ($\Omega$) that determines the boundary conditions.…
We consider the unitarity of the S-matrix for linearized General Relativity coupled to particle physics models. Taking renormalization group effects of the Planck mass into account, we find that the scale at which unitarity is violated is…
We present a solution method for the inverse scattering problem for integrable two-dimensional relativistic quantum field theories, specified in terms of a given massive single particle spectrum and a factorizing S-matrix. An arbitrary…
Planar N=4 super Yang-Mills appears to be integrable. While this allows to find this theory's exact spectrum, integrability has hitherto been of no direct use for scattering amplitudes. To remedy this, we deform all scattering amplitudes by…
A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…
In this review, we summarize the main ideas of perturbative algebraic quantum field theory, which is a rigorous framework combining some of the Haag-Kastler axioms with perturbative methods involving formal power series. It allows for the…
We present a non-perturbative regularization scheme for Quantum Field Theories which amounts to an embedding of the originally unregularized theory into a spacetime with an extra compactified dimensions of length L ~ Lambda^{-1} (with…
Networks of random quantum scatterers (S-matrices) form paradigmatic models for the propagation of coherent waves in random S-matrix network models cover universal localization-delocalization properties and have some advantages over more…
We describe a new regularization of quantum field theory on the noncommutative torus by means of one-dimensional matrix models. The construction is based on the Elliott-Evans inductive limit decomposition of the noncommutative torus…
We analyze the algebraic structure of $\phi_{1,2}$ perturbed minimal models relating them to graph-state models with an underlying Birman-Wenzl-Murakami algebra. Using this approach one can clarify some physical properties and reformulate…
We develop a formalism for the scattering of a particle on the $q$-deformed Euclidean space. We write down $q$-versions of the Lippmann-Schwinger equation. Their iterative solutions for a weak scattering potential lead us to $q$-versions of…
We present a study of the IR behaviour of a three-dimensional super-renormalisable quantum field theory (QFT) consisting of a scalar field in the adjoint of $SU(N)$ with a $\varphi^4$ interaction. A bare mass is required for the theory to…
We show that the matrix elements of integrable models computed by the Algebraic Bethe Ansatz can be put in direct correspondence with the Form Factors of integrable relativistic field theories. This happens when the S-matrix of a Bethe…
When massless particles are involved, the traditional scattering matrix ($S$-matrix) does not exist: it has no rigorous non-perturbative definition and has infrared divergences in its perturbative expansion. The problem can be traced to the…
Analytic perturbation theory for matrices and operators is an immensely useful mathematical technique. Most elementary introductions to this method have their background in the physics literature, and quantum mechanics in particular. In…
A natural procedure is introduced to replace the traditional, perturbatively generated counter terms to yield a formulation of covariant, self-interacting, nonrenormalizable scalar quantum field theories that has the added virtue of…
The quantum field theories (QFT) constructed in [1,2] include phenomenology of interest. The constructions approximate: scattering by $1/r$ and Yukawa potentials in non-relativistic approximations; and the first contributing order of the…
Changing some of its parameters over time is a paradigmatic way of driving an otherwise isolated many-body quantum system out of equilibrium, and a vital ingredient for building quantum computers and simulators. Here, we further develop a…
We present a {\sl non--perturbative} method, called {\sl Parametric Perturbation Theory} (PPT), which is alternative to the ordinary perturbation theory. The method relies on a principle of simplicity for the observable solutions, which are…