Related papers: Introduction to Pseudo-Group
Pseudopsin has been shown to be approximately conserved in nuclei. We investigate whether or not there is an advantage in using the pseudospin operators as well as the spin operators in the description of the nucleon-nucleon interaction. We…
Applications of the principle of reduction of couplings to the standard model and supersymmetric grand unified theories are reviewed. Phenomenological applications of renormalization group invariant sum rules for soft supersymmetry-breaking…
This paper has several purposes. We present through a critical review the results from already published papers on the constructive semigroup theory, and contribute to its further development by giving solutions to open problems. We also…
Pseudoalgebras, introduced in [BDK], are multi-dimensional analogues of conformal algebras, which provide an axiomatic description of the singular part of the operator product expansion. Our main interest in this paper is the pseudoalgebra…
A very elementary introduction to quantum algebras is presented and a few examples of their physical applications are mentioned.
Diagram semigroups are interesting algebraic and combinatorial objects, several types of them originating from questions in computer science and in physics. Here we describe diagram semigroups in a general framework and extend our…
This is an overview article on compact Lie groups and their representations, written for the Encyclopedia of Mathematical Physics to be published by Elsevier.
In [1, arXiv:1102.1844] the author disputes the conclusion of our paper [2, arXiv:1006.0714]. He claims that the Feynman graphs of three dimensional group field theory always represent pseudo manifolds. However, [1] uses a different…
We introduce an algebraic framework for interacting quantum systems that enables studying complex phenomena, characterized by the coexistence and competition of various broken symmetry states of matter. The approach unveils the hidden unity…
Various applications of quantum algebraic techniques in nuclear structure physics and in molecular physics are briefly reviewed and a recent application of these techniques to the structure of atomic clusters is discussed in more detail.
These lectures introduce key concepts in probability and statistical inference at a level suitable for graduate students in particle physics. Our goal is to paint as vivid a picture as possible of the concepts covered.
Current problems in particle physics are reviewed from the viewpoint of theories possessing extra spatial dimensions.
This introductory work combines bottom-up and top-down approaches towards understanding the underlying categorical structure of possible unifying theories descending from string theory. Guided by well-established developments in the realm…
This article reviews many manifestations and applications of dual representations of pairs of groups, primarily in atomic and nuclear physics. Examples are given to show how such paired representations are powerful aids in understanding the…
Generalized symmetries (also known as categorical symmetries) is a newly developing technique for studying quantum field theories. It has given us new insights into the structure of QFT and many new powerful tools that can be applied to the…
Quantum groups play the role of hidden symmetries of some two-dimensional field theories. We discuss how they appear in this role in the Wess-Zumino-Witten model of conformal field theory.
We define a class of quandle-like structures called pseudoquandles and analyze some of their algebraic properties.
The notion of pseudocategory, as considered in [11], is extended from the context of a 2-category to the more general one of a sesquicategory, which is considered as a category equipped with a 2-cell structure. Some particular examples of…
This text consists on a series of introductory lectures on cosmology for mathematicians and physicists who are not specialized on the subject.
A brief overview of the basic concepts and problems of the physics of quasi-one-dimensional compounds is done. Consistent theoretical description of the so-called pseudogap state remains the main problem. A simplified model of the pseudogap…