相关论文: Introducing Groups into Quantum Theory (1926 -- 19…

During the ``long decade'' of transformation of mathematical physics between 1915 and 1930, H. Weyl interacted with physics in two highly productive phases and contributed to it, among others, by his widely read book on {\em Space - Time -…

This is a self-contained review on the theory of quantum group and its applications to modern physics. A brief introduction is given to the Yang-Baxter equation in integrable quantum field theory and lattice statistical physics. The quantum…

Quantum groups emerged in the latter quarter of the 20th century as, on the one hand, a deep and natural generalisation of symmetry groups for certain integrable systems, and on the other as part of a generalisation of geometry itself…

We sketch a group-theoretical framework, based on the Heisenberg-Weyl group, encompassing both quantum and classical statistical descriptions of mechanical systems. We re-define in group-theoretical terms the kinematical arena and the…

In Part I of this series we presented the general ideas of applying group-algebraic methods for describing quantum systems. The treatment was there very "ascetic" in that only the structure of a locally compact topological group was used.…

Group Theory has become an invaluable tool in the physics community. Despite numerous introductory books, the subject remains challenging for beginners. Mathematica has emerged as a popular tool for research and education, offering various…

The scope of this review is to give a pedagogical introduction to some new calculations and methods developed by the author in the context of quantum groups and their applications. The review is self- contained and serves as a "first aid…

H. Weyl's proposal of 1918 for generalizing Riemannian geometry by local scale gauge (later called {\em Weyl geometry}) was motivated by mathematical, philosophical and physical considerations. It was the starting point of his unified field…

The theory of Non-Relativistic Quantum Mechanics was created (or discovered) back in the 1920's mainly by Schr\"odinger and Heisenberg, but it is fair enough to say that a more modern and unified approach to the subject was introduced by…

{We point out some obstacles raised by the lost of symmetry against the extension to the case of an interacting particle of the approach that {\sl deductively} establishes the Quantum Theory of a free particle according to the group…

One of the major developments of twentieth century physics has been the gradual recognition that a common feature of the known fundamental interactions is their gauge structure. In this talk the early history of gauge theory is reviewed,…

There is a unique finite group that lies inside the 2-dimensional unitary group but not in the special unitary group, and maps by the symmetric square to an irreducible subgroup of the 3-dimensional real special orthogonal group. In an…

In this work, we present straightforward and concrete computations of the unitary irreducible representations of the Euclidean motion group $M(2)$ employing the methods of deformation quantization. Deformation quantization is a quantization…

Group theory is used in many textbooks of contemporary physics. However, electromagnetic community often considers group theory as an "exotic" tool. Graduate and postgraduate textbooks on electromagnetics and electrodynamics usually do not…

A new picture of Quantum Mechanics based on the theory of groupoids is presented. This picture provides the mathematical background for Schwinger's algebra of selective measurements and helps to understand its scope and eventual…

In this paper we present a survey of the use of differential geometric formalisms to describe Quantum Mechanics. We analyze Schroedinger and Heisenberg frameworks from this perspective and discuss how the momentum map associated to the…

I review the various algebraic foundations of quantum mechanics. They have been suggested since the birth of this theory till up to last year. They are the following ones: Heisenberg-Born-Jordan (1925), Weyl (1928), Dirac (1930), von…

Introductive backgrounds of a new mathematical physics discipline - Quantum Mathematics - are discussed and analyzed both from historical and analytical points of view. The magic properties of the second quantization method, invented by V.…

The paper provides an introduction into p-mechanics, which is a consistent physical theory suitable for a simultaneous description of classical and quantum mechanics. p-Mechanics naturally provides a common ground for several different…

Few, if any, applications of quantum technology are as widely known as the quantum simulation of quantum matter. Consequently, many interesting questions have been sparked at the intersection of condensed matter, quantum chemistry, and…