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The currently accepted mathematical description of the fundamental constituents and interactions of matter is the Standard Model of particle physics. Its last missing particle, the famous Higgs boson, was observed at the Large Hadron…
One of the interesting aspects in the study of atomic nuclei is the strikingly regular behaviour many display in spite of being complex quantum-mechanical systems, prompting the universal question of how regularity emerges out of…
With the discovery of the Higgs boson the LHC experiments have closed the most important gap in our understanding of fundamental interactions. We now know that the interactions between elementary particles can be described by quantum field…
These notes form part of a lecture course on gauge theory. The material covered is standard in the physics literature, but perhaps less well-known to mathematicians. The purpose of these notes is to make spontaneous symmetry breaking and…
From the humble beginnings of particle physics to groundbreaking discoveries, the journey of particle physics has revolutionized our understanding of the universe. The progression of particle physics, begin from the discovery of new…
The main ideas behind nuclear supersymmetry are presented, starting from the basic concepts of symmetry and the methods of group theory in physics. We propose new, more stringent experimental tests that probe the supersymmetry…
The particle filter is a powerful framework for estimating hidden states in dynamic systems where uncertainty, noise, and nonlinearity dominate. This mini-book offers a clear and structured introduction to the core ideas behind particle…
We provide a pedagogical introduction to $N=1$ supergravity/supersymmetry in relation to particle physics. The various steps in the construction of a generic $N=1$ supergravity model are briefly described, and we focus on its low energy…
The job of a physicist is to describe Nature. General features, hypotheses and theories help to describe physics phenomena at a more abstract, fundamental level, and are sometimes tacitly assigned some sort of real existence; doing so…
I start with a brief introduction to the elementary particles and their interactions, Higgs mechanism and supersymmetry. The major physics objectives of the Tevatron and LHC colliders are identified. The status and prospects of the top…
These summer school lectures cover the use of algebraic techniques in various subfields of nuclear physics. After a brief description of groups and algebras, concepts of dynamical symmetry, dynamical supersymmetry, and supersymmetric…
These notes were compiled as lecture notes for a course developed and taught at the University of the Southern California. They should be accessible to a typical engineering graduate student with a strong background in Applied Mathematics.…
These notes are an expanded version of a short course of lectures given for graduate students in particle physics at Oxford. The level was intended to be appropriate for students in both experimental and theoretical particle physics.The…
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…
These notes are intended to provide an introduction to supersymmetry. The notes begin with supersymmetric quantum mechanics and the basic properties of spinor fields. The supersymmetry of simple theories of spin-zero and spin-one-half…
Written in non-technical language, this review article explains the significance of the Higgs field and the associated Higgs boson in High-Energy Physics. The connection of symmetry with particle interactions and their unification is also…
These lecture notes review the theoretical background to the Higgs boson, provide an introduction to its phenomenology, and describe the experimental tests that lead us to think that "beyond any reasonable doubt, it is a Higgs boson".…
The basic ingredients of the Spontaneous Symmetry Breaking Phenomenon and of the Higgs Mechanism are reviewed in these lectures of pedagogical character. Some relevant topics related with the breaking $\gs \rightarrow U(1)_{\rm em}$ are…
Particle physics has evolved a coherent model that characterizes forces and particles at the most elementary level. This Standard Model, built from many theoretical and experimental studies, is in excellent accord with almost all current…
The current description of fundamental interactions is based on two theories with the status of standard models. The electromagnetic and nuclear interactions are described at a quantum level by the Standard Model of particle physics, using…