Related papers: Scattering in geometric approach to quantum theory
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…
This review is a primer on recently established geometric methods for observables in quantum field theories. The main emphasis is on amplituhedra, i.e. geometries encoding scattering amplitudes for a variety of theories. These pertain to a…
A self-contained discussion of nonrelativistic quantum scattering is presented in the case of central potentials in one space dimension, which will facilitate the understanding of the more complex scattering theory in two and three…
We construct a scattering theory for harmonic one-forms on Riemann surfaces, obtained from boundary value problems involving systems of curves and the jump problem. We obtain an explicit expression for the scattering matrix in terms of…
A number of studies have shown that chaos occurs in scattering: the outgoing deflection angle is seen to be an erratic function of the impact parameter. We propose to extend this to quantum field theory, and to use erratic behavior of the…
Scattering amplitudes are both a wonderful playground to discover novel ideas in Quantum Field Theory and simultaneously of immense phenomenological importance to make precision predictions for e.g.~particle collider observables and more…
We investigate factorized scattering from a reflecting and transmitting impurity. Bulk scattering is non trivial, provided that the bulk scattering matrix depends separately on the spectral parameters of the colliding particles, and not…
It has been proposed that the incorporation of an observer independent minimal length scale into the quantum field theories of the standard model effectively describes phenomenological aspects of quantum gravity. The aim of this paper is to…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
The kinematical setting of spherically symmetric quantum geometry, derived from the full theory of loop quantum gravity, is developed. This extends previous studies of homogeneous models to inhomogeneous ones where interesting field theory…
We present a new model of quantum gravity as a theory of random geometries given explicitly in terms of a multitrace matrix model. This is a generalization of the usual discretized random surfaces of 2D quantum gravity which works away from…
Conventional approaches for scattering manipulations rely on the technique of field expansions into spherical harmonics (electromagnetic multipoles), which nevertheless is non-generic (expansion coefficients depend on the position of the…
This work deals with the average scattering entropy of quantum graphs. We explore this concept in several distinct scenarios that involve periodic, aperiodic and random distribution of vertices of distinct degrees. In particular, we compare…
Algebraic quantum field theory is a general mathematical framework for relativistic quantum physics, based on the theory of operator algebras. It comprises all observable and operational aspects of a theory. In its framework the entire…
In this work, we discuss the scattering theory of local, relativistic quantum fields with indefinite metric. Since the results of Haag--Ruelle theory do not carry over to the case of indefinite metric, we propose an axiomatic framework for…
Quantum scattering is studied in a system consisting of randomly distributed point scatterers in the strip. The model is continuous yet exactly solvable. Varying the number of scatterers (the sample length) we investigate a transition…
In gravitational scattering the quantum particle probes the Fourier-transforms of a metric. I evaluate the Fourier-transforms of Schwarzschild metrics in standard, harmonic and other coordinate systems in linear and $G^2-$approximations. In…
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…
In this article we review the basic concepts regarding quantum integrability. Special emphasis is given on the algebraic content of integrable models. The associated algebras are essentially described by the Yang-Baxter and boundary…
The basic elements of the geometric approach to a consistent quantization formalism are summarized, with reference to the methods of the old quantum mechanics and the induced representations theory of Lie groups. A possible relationship…