Physics Commons^™

Particle Dynamics In Anti-De Sitter Space By Eih Method, Jiusi Lei

Dissertations, Theses, and Capstone Projects

Following the work of Einstein, Infeld and Hoffmann, we show that particle dynamics in Anti-de Sitter spacetime can be built up by regarding singularities in spacetime manifold as the source of particles.

Since gauge fields play a foundational role in the action, the singularities are chosen to be point-like instantons. Their winding number, defined by an integration on the spheres surrounding those singularities, will turn out to be related to their masses. And their action, derived from the Chern-Simons forms, will be a co-adjoint orbit action, with group element g ∈ SO(4, 2) describing the collective coordinates of the particle. …

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 …