Related papers: Relativistic Theory of Infinite Statistics Fields
Symmetries are playing a very prominent role in natural sciences. In mathematics as the language of physics, symmetries are treated within the framework of group theory, which provides the tools to classify natural laws and physical objects…
A system of interacting atoms is represented as an union of two subsystems, one of which is the system of atoms, and the other is an auxiliary scalar covariant field, which is equivalent to a given static interatomic potential of general…
We comment on the present status, the concepts and their limitations, and the successes and open problems of the various approaches to a relativistic quantum theory of elementary particles, with a hindsight to questions concerning quantum…
Although Quantum field theory has been very successful in explaining experiment, there are two aspects of the theory that remain quite troubling. One is the no-interaction result proved in Haag's theorem. The other is the existence of…
The existence of a classical limit describing interacting particles in a second-quantized theory of identical particles with bosonic symmetry is proved. This limit exists in addition to a previously established classical limit with a…
The state space and observables for the leading order of the large-N theory are constructed. The obtained model ("theory of infinite number of fields") is shown to obey Wightman-type axioms (including invariance under boost transformations)…
Today it still remains a challenge whether quantum mechanics has an underlying statistical explanation or not. While there are and were a lot of models trying to explain quantum phenomena with statistical methods these all failed on certain…
A realistic physical axiomatic approach of the relativistic quantum field theory is presented. Following the action principle of Schwinger, a covariant and general formulation is obtained. The correspondence principle is not invoked and the…
Representation theory is shown to be incomplete in terms of enumerating all integrable limits of quantum systems. As a consequence, one can find exactly solvable Hamiltonians which have apparently strongly broken symmetry. The number of…
Counting the number of clusters, when these clusters overlap significantly is a challenging problem in machine learning. We argue that a purely mathematical quantum theory, formulated using the path integral technique, when applied to…
The geometric form of standard quantum mechanics is compatible with the two postulates: 1) The laws of physics are invariant under the choice of experimental setup and 2) Every quantum observation or event is intrinsically statistical.…
Quantum field theory offers physicists a tremendously wide range of application; it is both a language with which a vast variety of physical processes can be discussed and also it provides a model for fundamental physics, the so-called…
We review various aspects of (infinite) quantum group symmetries in 2D massive quantum field theories. We discuss how these symmetries can be used to exactly solve the integrable models. A possible way for generalizing to three dimensions…
Quantum field theory is mostly known as the most advanced and well-developed theory in physics, which combines quantum mechanics and special relativity consistently. In this work, we study the spinless quantum field theory, namely the…
The aim of the paper is to derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The main extensions, which also can be motivated from an applied statistics point…
The apparent impossibility of extending non-relativistic quantum mechanics to a relativistic quantum theory is shown to be due to the insufficient structural richness of the field of complex numbers over which quantum mechanics is built. A…
We study quantum field models in indefinite metric. We introduce the modified Wightman axioms of Morchio and Strocchi as a general framework of indefinite metric quantum field theory (QFT) and present concrete interacting relativistic…
An Ising-type classical statistical ensemble can describe the quantum physics of fermions if one chooses a particular law for the time evolution of the probability distribution. It accounts for the time evolution of a quantum field theory…
I describe how integrable quantum field theories in 2 spacetime dimensions are characterized by infinite dimensional quantum group symmetries, namely the q-deformations of affine Lie algebras, and their Yangian limit. These symmetries can…
This article aims to explain some of the basic facts about the questions raised in the title, without the technical details that are available in the literature. We provide a gentle introduction to some rather classical results about…