Algebra Commons^™

Classification Of Topological Defects In Cosmological Models, Abigail Swanson

Student Research Submissions

In nature, symmetries play an extremely significant role. Understanding the symmetries of a system can tell us important information and help us make predictions. However, these symmetries can break and form a new type of symmetry in the system. Most notably, this occurs when the system goes through a phase transition. Sometimes, a symmetry can break and produce a tear, known as a topological defect, in the system. These defects cannot be removed through a continuous transformation and can have major consequences on the system as a whole. It is helpful to know what type of defect is produced when …

General Covariance With Stacks And The Batalin-Vilkovisky Formalism, Filip Dul

Doctoral Dissertations

In this thesis we develop a formulation of general covariance, an essential property for many field theories on curved spacetimes, using the language of stacks and the Batalin-Vilkovisky formalism. We survey the theory of stacks, both from a global and formal perspective, and consider the key example in our work: the moduli stack of metrics modulo diffeomorphism. This is then coupled to the Batalin-Vilkovisky formalism–a formulation of field theory motivated by developments in derived geometry–to describe the associated equivariant observables of a theory and to recover and generalize results regarding current conservation.

The Differentialgeometry Package, Ian M. Anderson, Charles G. Torre

Downloads

This is the entire DifferentialGeometry package, a zip file (DifferentialGeometry.zip) containing (1) a Maple Library file, DifferentialGeometryUSU.mla, (2) a Maple help file DifferentialGeometry.help, (3) a Maple Library file, DGApplicatons.mla. This is the latest version of the DifferentialGeometry software; it supersedes what is released with Maple.

Installation instructions

Spacetime Groups, Ian M. Anderson, Charles G. Torre

Publications

A spacetime group is a connected 4-dimensional Lie group G endowed with a left invariant Lorentz metric h and such that the connected component of the isometry group of h is G itself. The Newman-Penrose formalism is used to give an algebraic classification of spacetime groups, that is, we determine a complete list of inequivalent spacetime Lie algebras, which are pairs (g,η), with g being a 4-dimensional Lie algebra and η being a Lorentzian inner product on g. A full analysis of the equivalence problem for spacetime Lie algebras is given which leads to a completely algorithmic solution to the …

Some 2-Categorical Aspects In Physics, Arthur Parzygnat

Dissertations, Theses, and Capstone Projects

2-categories provide a useful transition point between ordinary category theory and infinity-category theory where one can perform concrete computations for applications in physics and at the same time provide rigorous formalism for mathematical structures appearing in physics. We survey three such broad instances. First, we describe two-dimensional algebra as a means of constructing non-abelian parallel transport along surfaces which can be used to describe strings charged under non-abelian gauge groups in string theory. Second, we formalize the notion of convex and cone categories, provide a preliminary categorical definition of entropy, and exhibit several examples. Thirdly, we provide a universal description …

How To Create A Lie Algebra, Ian M. Anderson

How to... in 10 minutes or less

We show how to create a Lie algebra in Maple using three of the most common approaches: matrices, vector fields and structure equations. PDF and Maple worksheets can be downloaded from the links below.

Introduction Aux Méthodes D’Intégrale De Chemin Et Applications, Nour-Eddiine Fahssi

Nour-Eddine Fahssi

These lecture notes are based on a master course given at University Hassan II - Agdal in spring 2012.

Some Irrational Generalised Moonshine From Orbifolds, Rossen Ivanov, Michael Tuite

Articles

We verify the Generalised Moonshine conjectures for some irrational modular functions for theMonster centralisers related to the Harada-Norton, Held, M12 and L3(3) simple groups based on certain orbifolding constraints. We find explicitly the fixing groups of the hauptmoduls arising in each case.

Rational Generalized Moonshine From Abelian Orbifoldings Of The Moonshine Module, Rossen Ivanov, Michael Tuite

Articles

We consider orbifoldings of the Moonshine Module with respect to the abelian group generated by a pair of commuting Monster group elements with one of prime order p = 2, 3, 5, 7 and the other of order pk for k = 1 or k prime. We show that constraints arising from meromorphic orbifold conformal field theory allow us to demonstrate that each orbifold partition function with rational coefficients is either constant or is a hauptmodul for an explicitly found modular fixing group of genus zero. We thus confirm in the cases considered the Generalised Moonshine conjectures for all rational …