Related papers: Introduction to abelian anyons in planar systems
The theory of causal fermion systems is an approach to describe fundamental physics. We here introduce the mathematical framework and give an overview of the objectives and current results.
The present paper refers to the theory and the practice of the systems regarding non-linear systems and their applications. We aimed the integration of these systems to elaborate their response as well as to highlight some outstanding…
We survey recent developments in the Birational Anabelian Geometry program aimed at the reconstruction of function fields of algebraic varieties over algebraically closed fields from pieces of their absolute Galois groups.
A realistic axiomatic formulation of Galilean Quantum Field Theories is presented, from which the most important theorems of the theory can be deduced. In comparison with others formulations, the formal aspect has been improved by the use…
After a review on the development of deformation theory of abelian complex structures from both the classical and generalized sense, we propose the concept of semi-abelian generalized complex structure. We present some observations on such…
In bosonic end perturbative calculations for quantum mechanical anyon systems a regularization and renormalization procedure, analogous to those used in field theory, is necessary. I examine the reliability and the physical interpretation…
The commutation relations of the composite fields are studied in the 3, 2 and 1 space dimensions. It is shown that the field of an atom consisting of a nucleus and an electron fields satisfies, in the space-like asymptotic limit, the…
A model about excited field of a particle is discussed. We found this model will give wave-particle duality clearly and its Lagrangian is consistent with Quantum Theory. A new interpretation of quantum mechanics but not statistical…
A structure theorem is proved for strongly holonomic modules over a quantum torus (a crossed product of a field with a free abelian group in which the field is central). This can be applied to give a structure theorem for finitely presented…
There is debate as to whether quantum field theory is, at bottom, a quantum theory of fields or particles. One can take a field approach to the theory, using wave functionals over field configurations, or a particle approach, using wave…
The anomaly of a quantum field theory is an expression of its projective nature. This starting point quickly leads to its manifestation as a special kind of field theory: a once-categorified invertible theory. We arrive at this statement…
A survey is given on the present status of analytic calculation methods and the mathematical structures of zero- and single scale Feynman amplitudes which emerge in higher order perturbative calculations in the Standard Model of elementary…
The aim of this paper is to give an introduction to our axiomatic logical analysis of relativity theories.
An algebraic formalism for the study of a system of charged particles interacting with an external quantum field is developed. The notion of monoidal categories with duality is used for the description of composite systems and corresponding…
In this work we provide a comprehensive review of theoretical and experimental studies of the properties of polarons formed by mobile impurities strongly interacting with quantum many-body systems. We present a unified perspective on the…
The quantum mechanics formalism introduced new revolutionary concepts challenging our everyday perceptions. Arguably, quantum entanglement, which explains correlations that cannot be reproduced classically, is the most notable of them.…
Anyons are quasiparticles in two-dimensional systems that show statistical properties very distinct from those of bosons or fermions. While their isolated observation has not yet been achieved, here we perform a quantum simulation of anyons…
We propose novel infrared dualities connecting 2+1 dimensional non-Abelian gauge theories (with unitary or special unitary gauge groups) to Abelian gauge theories. The dual Abelian theories are characterized by a planar quiver structure,…
We show that excitations in a recently proposed gauge theory for anyons on a line in fact do not obey anomalous statistics. On the other hand, the theory supports novel chiral solitons. Also we construct a field-theoretic description of…
I discuss my recent attempt in search of a new framework for quantum field theory of D branes. After explaining some motivations in the background of this project, I present, as a first step towards our goal, a second-quantized…