Kinematical algebras in a non-relativistic expansion of the Lorentz force

Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2023, Tutors: Joaquim Gomis, Jorge RussoWe consider a non-relativistic expansion of the Lorentz force equation. Both the particle position and the electro-magnetic field are expanded. There are two interesting limits in the case of a constant field, called electric and magnetic, where we show that the resulting equations also follow from considering a non-linear realisation of a certain infinite-dimensional algebra

Renormalizability of Yang-Mills in R4\mathbb{R}^4

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2023, Director: Ignasi Mundet i Riera[en] The present work is an attempt to introduce a novel axiomatic formulation of Quantum Field Theory proposed by Kevin Costello in [Cos11. Far from being exhaustive, we aim to present the main results and constructions, followed by calculations in this formalism that match the physics literature. We try to give a pedagogical introduction, providing all the definitions that an undergraduate student would need to understand the key concepts. We start by defining the simplest kinds of quantum field theories and how to make sense of divergent quantities. As we move forward, we try to generalize these definitions to more and more general classes of theories. The endpoint of this work is to use Costello's machinery to define the Yang-Mills theory on $\mathbb{R}^4$ and prove that it is perturbatively renormalizable