Related papers: Lie Groups and their applications to Particle Phys…
The goal of these lectures is to give an introduction to the study of the fundamental group of a Klein surface. We start by reviewing the topological classification of Klein surfaces and by explaining the relation with real algebraic…
Lie group theory states that knowledge of a $m$-parameters solvable group of symmetries of a system of ordinary differential equations allows to reduce by $m$ the number of equation. We apply this principle by finding dilatations and…
An unconventional outlook on relationship between the quantum mechanics and special relativity is proposed. We show that the two fundamental postulates of quantum mechanics of Planck and de Broglie combined with the idea of comparison scale…
Lie-symmetry methods are used to determine the symmetry group of reduced magnetohydrodynamics. This group allows for arbitrary, continuous transformations of the fields themselves, along with space-time transformations. The derivation…
Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical…
This paper introduces Lie groups in degenerate geometric (Clifford) algebras that preserve four fundamental subspaces determined by the grade involution and reversion under the adjoint and twisted adjoint representations. We prove that…
Group theory (GT) provides a rigorous framework for studying symmetries in various disciplines in physics ranging from quantum field theories and the standard model to fluid mechanics and chaos theory. To date, the application of such a…
These notes are an outgrowth of an advanced undergraduate course taught at the University of Maryland, College Park. They are intended as an introduction to various aspects of particle and nuclear physics with an emphasis on the role of…
Depending on the point of view, modern machine learning is either providing an unprecedented boost to the numerical methods of particle physics, or it is transforming the way we do science with vast amounts of complex data. In any case, it…
We give a short and elementary introduction to Lie group methods. A selection of applications of Lie group integrators are discussed. Finally, a family of symplectic integrators on cotangent bundles of Lie groups is presented and the notion…
Wigner's classification has led to the insight that projective unitary representations play a prominent role in quantum mechanics. The physics literature often states that the theory of projective unitary representations can be reduced to…
The problem of detecting and quantifying the presence of symmetries in datasets is useful for model selection, generative modeling, and data analysis, amongst others. While existing methods for hard-coding transformations in neural networks…
It is shown that the correct mathematical implementation of symmetry in the geometric formulation of classical field theory leads naturally beyond the concept of Lie groups and their actions on manifolds, out into the realm of Lie group…
The theory of Lie systems has recently been applied to Quantum Mechanics and additionally some integrability conditions for Lie systems of differential equations have also recently been analysed from a geometric perspective. In this paper…
This paper provides a modern presentation of Noether's theory in the realm of classical dynamics, with application to the problem of a particle submitted to both a potential and a linear dissipation. After a review of the close…
This note provides a formula for the character of the Lie algebra of the fundamental group of a surface, viewed as a module over the symplectic group.
In Norway, particle physics is part of the high school curriculum in physics which introduces the need for good university teaching in particle physics without the usual technical approach. Given how much conflicting information and…
Some very elementary ideas about quantum groups and quantum algebras are introduced and a few examples of their physical applications are mentioned.
These five lectures collect elementary facts about 4D supersymmetric theories with emphasis on N=1 supersymmetry, as well as the basic notions of supersymmetric quantum mechanics. Contents: I. From symmetries to supersymmetry; II. Basic…
In this pedagogical article, we explore a powerful language for describing the notion of spacetime and particle dynamics intrinsic to a given fundamental physical theory, focusing on special relativity and its Newtonian limit. The starting…