Operators, matrices, and group theory

C. Quesne

Lenny Bueno Guzmán, Julio Antonio Manzueta

A research study was carried out, it has as its fundamental objective, the Pauli Matrices to determine the Spin of a Particle from the perspective of Group Theory. This, in turn, is structured in five chapters, within which are elements such as the antecedents related to the line of research, the approach to the problem, the justification of said problem, as well as the scope and limits of It has a referential framework, where the fundamental concepts for its development are illustrated, after the research methodology is expressed, the results obtained are presented and finally conclusions that respond to the objectives are illustrated. It has a methodology, framed in the analytical method, since the Pauli Matrices and the Group Theory were analyzed, in addition, it started from general aspects, to reach particular conclusions. In it, a non-experimental design was developed, because variables were not manipulated, and also exploratory because the subject has been little studied. In the development of this document some interesting elements are highlighted, among which we can highlight; the Pauli matrices to determine the behavior of a particle, the vector operators, the use of Hermitian operators, the characteristics of these operators from the perspective of Group Theory, the theorems, their properties and propositions.

Leo de Wit

Scattering processes are a standard topic covered in introductory courses on quantum mechanics and particle physics. Unfortunately, a full mathematical treatment tends to be overwhelming for undergraduate students. This article introduces some toy models that are easy to comprehend but still contain the essential features of quantum theory. We define a Hilbert space with state vectors and use creation/annihilation operators to construct transition matrices and S-matrices. We show how perturbation theory gives rise to Feynman diagrams and Feynman rules. We also discuss how we can use symmetry and group theory to restrict what interactions are possible.

V. Balakrishnan

Saidakbar Kh. Abdukhakimov, Makhmud B. Bayzakov

Boost matrices, eigenvalues, group factorization, Lorentz group, orthosymplectic matrices, squeezing matrices, Michelson-Morley experiment, FitzGerald-Lorentz contraction, history of special relativity, Lorentz-Poincar ether theory

George C. Turrell