Related papers: Particle Physics: a crash course for Mathematician…
We systematically include central charges into supersymmetric quantum mechanics formulated on curved Euclidean spaces, and explain how the background geometry manifests itself on states of the theory. In particular, we show in detail how,…
The Standard Model of particle physics may seem complicated and arbitrary, but it has hidden patterns that are revealed by the relationship between three "grand unified theories": theories that unify forces and particles by extending the…
Expansion of the categorical point of view on many areas of the mathematics and mathematical physics will cause to deeper understanding of genuine features of these problems. New applications of categorical methods are connected with new…
The standard model of particle physics is marvelously successful. However, it is obviously not a complete or final theory. I shall argue here that the structure of the standard model gives some quite concrete, compelling hints regarding…
We briefly overview how, historically, string theory led theoretical physics first to precise problems in algebraic and differential geometry, and thence to computational geometry in the last decade or so, and now, in the last few years, to…
The unification of Quantum Mechanics and General Relativity remains the primary goal of Theoretical Physics, with string theory appearing as the only plausible unifying scheme. In the present work, in a search of the conceptual foundations…
We give a brief overview on the successes and theoretical problems of the Standard Model and discuss the basics of low-scale supersymmetry. We also address some of recent proposals for physics beyond the Standard Model and the connection to…
The present article deals with general mechanics in an unconventional manner. At first, Newtonian mechanics for a point particle has been described in vectorial picture, considering Cartesian, polar and tangent-normal formulations in a…
Recent ideas on modular localization in local quantum physics are used to clarify the relation between on- and off-shell quantities in particle physics; in particular the relation between on-shell crossing symmetry and off-shell Einstein…
Our starting point is a particular `canvas' aimed to `draw' theories of physics, which has symmetric monoidal categories as its mathematical backbone. In this paper we consider the conceptual foundations for this canvas, and how these can…
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…
A central aim of theoretical physics is to account for the structure of matter at the most elementary level as underlying the Standard Model of particle physics, and ideally also as a basis for a substantial dark sector, as distributed in…
We develop classical globally supersymmetric theories. As much as possible, we treat various dimensions and various amounts of supersymmetry in a uniform manner. We discuss theories both in components and in superspace. Throughout we…
An introduction to spin techniques in particle physics is given. Among the topics covered are: helicity formalism and its applications to the decay and scattering of spin-1/2 and spin-1 particles, techniques for evaluating helicity…
Geometrical formulation of classical mechanics with forces that are not necessarily potential-generated is presented. It is shown that a natural geometrical "playground" for a mechanical system of point particles lacking Lagrangian and/or…
Generalized symmetries (also known as categorical symmetries) is a newly developing technique for studying quantum field theories. It has given us new insights into the structure of QFT and many new powerful tools that can be applied to the…
Expanding the results of [1], [2], [3], we demonstrate a network of algebraic connections between six well-known particle theories. These are the Spin(10) model, the Georgi-Glashow model, the Pati-Salam model, the Left-Right Symmetric…
In this paper we introduce elements of algebraic geometry over an arbitrary algebraic structure. We prove Unification Theorems which gather the description of coordinate algebras by several ways.
Recent critiques of the semantic conception of scientific theories suggest that a theory is not best formulated as a collection of models satisfying some set of kinematical or dynamical conditions. Thus it has been argued that additional…
These lectures introduce the basic ideas and practices of statistical analysis for particle physicists, using a real-world example to illustrate how the abstractions on which statistics is based are translated into practical application.