Related papers: A Brief Introduction to Particle Interactions
Following the approach of Grignani and Nardelli [1], we show how to cast the two-dimensional model $L \sim curv^2 + torsion^2 + cosm.const$ -- and in fact any theory of gravity -- into the form of a Poincare gauge theory. By means of the…
These lecture notes are from a first course on the Minimal Supersymmetric Standard Model. The level of the notes is introductory and pedagogical. Standard Model, basic supersymmetry algebra and its representations are considered as…
We show that Calogero-Sutherland models for interacting particles have a natural supersymmetric extension. For the construction, we use Jacobians which appear in certain superspaces. Some of the resulting Hamiltonians have a direct physics…
Our present understanding of elementary particle interactions is the synergic result of developments of theoretical ideas and of experimental advances that lead to the theory known as the Standard Model of particle physics. Despite the…
This book is mainly an exposition of the author's works and his joint works with his former students on explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic…
The main result of this article is an application of the theory of invariant convex cones of Lie algebras to the study of unitary representations of Lie supergroups. It also includes an exposition of recent results of the second author on…
The aim of this paper is to discuss a kinematical algebraic structure of a theory of gravity, that would be unitary, renormalizable and coupled in the same manner to both spinorial and tensorial matter fields. An analysis of the common…
A generalized algebra of quantum observables, depending on extra dimensional constants, is considered. Some limiting forms of the algebra are investigated and their possible applications to the descriptions of interactions of fundamental…
The quest for unification of particles and fields and for reconciliation of Quantum Mechanics and General Relativity has led us to gauge theories, string theories, supersymmetry and higher-extended objects: membranes... Our spacetime is…
These lectures are a brief introduction to supersymmetry.
In these lectures, I discuss the role of symmetries in particle physics. I begin by discussing global symmetries and show that they can be realized differently in nature, depending on whether or not the vacuum state is left invariant by the…
This introduction to Lifshitz-type field theories reviews some of its aspects in Particle Physics. Attractive features of these models are described with different examples, as the improvement of graphs convergence, the introduction of new…
This lecture reviews the principles of particle-matter interactions, providing the essential physics background required to understand beam loss mechanisms in high-energy accelerators and their associated implications. The main interaction…
The concept of symmetries in physics is briefly reviewed. In the first part of these lecture notes, some of the basic mathematical tools needed for the understanding of symmetries in nature are presented, namely group theory, Lie groups and…
The most general 2+1 dimensional spinning particle model is considered. The action functional may involve all the possible first order Poincare invariants of world lines, and the particular class of actions is specified thus the…
It is argued that substantial portions of both Newtonian particle mechanics and general relativity can be viewed as relational (rather than absolute) theories. I furthermore use the relational particle models as toy models to investigate…
We consider the interaction of gravity, as expressed by Einstein's Equations of General Relativity, to other force fields. We describe some recent results, discussing both the mathematics, and the physical interpretations. These results…
In the recent years, Hopf algebras have been introduced to describe certain combinatorial properties of quantum field theories. I will give a basic introduction to these algebras and review some occurrences in particle physics.
The interactions inside the (bisemi)particles are envisaged from two points of view: The first approach, based on the reducible representations of algebraic bilinear semigroups, allows to describe explicitly the interactions between…
Using a Poisson bracket representation, in 3D, of the Lie algebra $\mathfrak{sl}(2)$, we first use highest weight representations to embed this into larger Lie algebras. These are then interpreted as symmetry and conformal symmetry algebras…