Related papers: Scattering in geometric approach to quantum theory
In this note, we explore some recent advancements in enumerative algebraic geometry, focusing particularly on the role of quantum K-theory of quiver varieties as viewed through the lens of integrable systems. We highlight a number of…
Recently, the theory of symmetric spaces has come to play an increased role in the physics of integrable systems and in quantum transport problems. In addition, it provides a classification of random matrix theories. In this paper we give a…
We analyze some consequences of two possible interpretations of the action of the ladder operators emerging from generalized Heisenberg algebras in the framework of the second quantized formalism. Within the first interpretation we…
The goal of this paper is to make a connection between tropical geometry, representations of quantum affine algebras, and scattering amplitudes in physics. The connection allows us to study important and difficult questions in these areas:…
We present a systematic formulation of scattering theory for nonlinear interactions in one dimension and develop a nonlinear generalization of the transfer matrix that has a composition property similar to its linear analog's. We offer…
We study the $S$-matrix interpretation of quantum theory in light of Categotical Quantum Mechanics. The $S$-matrix interpretation of quantum theory is shown to be a functorial semantics relating the algebras of quantum theory to the…
A non-relativistic scalar particle moving on a curved surface undergoes a geometric scattering whose behavior is sensitive to the theoretically ambiguous values of the intrinsic and extrinsic curvature coefficients entering the expression…
Scattering amplitudes in quantum field theory are independent of the field parameterization, which has a natural geometric interpretation as a form of `coordinate invariance.' Amplitudes can be expressed in terms of Riemannian curvature…
The field of scattering amplitudes plays a central role in elementary-particle physics. This includes various problems of broader interest for collider physics, gravitational physics, and fundamental principles underlying quantum field…
We discuss possible applications of the 1-D direct and inverse scattering problem to design of universal quantum gates for quantum computation. The potentials generating some universal gates are described.
Motivated by the limited interaction between the mathematical physics community and theoretical physicists - particularly in high-energy theory - we present a computation that is typically the first example in QFT courses but, to our…
Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We develop a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory…
Viewing gravitational energy-momentum as equal by observation, but different in essence from inertial energy-momentum naturally leads to the gauge theory of volume-preserving diffeormorphisms of a four-dimensional in- ner space. To analyse…
`How do our ideas about quantum mechanics affect our understanding of spacetime?' This familiar question leads to quantum gravity. The complementary question is also important: `How do our ideas about spacetime affect our understanding of…
In the scattering theory framework, we point out a connection between the spectrum of the scattering matrix of two operators and the spectrum of the difference of spectral projections of these operators.
The scattering of free particles constrained to move on a cylindrically symmetric curved surface is studied. The nontrivial geometry of the space contributes to the scattering cross section through the kinetic as well as a possible scalar…
We review the main features of a mathematical framework encompassing some of the salient quantum mechanical and geometrical aspects of Hall systems with finite size and general boundary conditions. Geometrical as well as algebraic…
Universality in physics describes how disparate systems can exhibit identical low-energy behavior. Here, we reveal a rich landscape of new universal scattering phenomena governed by the interplay between an interaction and a system's…
Scattering amplitudes in quantum field theories are of widespread interest, due to a large number of theoretical and phenomenological applications. Much is known about the possible behaviour of amplitudes, that is independent of the details…
Goal of this review is to introduce the algebraic approach to quantum field theory on curved backgrounds. Based on a set of axioms, first written down by Haag and Kastler, this method consists of a two-step procedure. In the first one, a…