Abstract
These notes are an outgrowth of an advanced undergraduate course taught at the University of Maryland, College Park. They are intended as an introduction to various aspects of particle and nuclear physics with an emphasis on the role of symmetry. The basic philosophy is to introduce many of the fundamental ideas in nuclear and particle physics using relatively sophisticated mathematical tools -- but to do so in as a simplified a context to explain the underlying ideas. Thus, for example, the Higgs mechanism is discussed in terms of an Abelian Higgs model. The emphasis is largely, but not entirely theoretical in orientation. The goal is for readers to develop an understanding of many of the underlying issues in a relatively sophisticated way.
Highlights
We have shown that the particles described by this scalar field theory are bosons!! Given this tremendous success, it is time to turn to fermions
If we look at the hydrogen atom from far away and forget that it is a composite system made of smaller individual particles, it looks like you have one big particle with an intrinsic negative parity
This means that if we have a solution to the Schrödinger equation ψ, we can locally twist its phase to ψ, which is guaranteed to be another solution to the Schrödinger equation with a gauge-transformed version of the potentials
Summary
If one were to ask a contemporary physicist for a simple cartoon overview of our current understanding of fundamental physics they would probably give something like Fig. 1. Rutherford had a brilliant insight: instead of passively studying matter by looking at how some types of matter emit radioactive particles, one could use radioactivity as a probe of matter He designed an experiment carried out at the University of Manchester by a postdoctoral scientist Geiger (of Geiger counter fame) and an undergraduate Marsden, in which α radiation impinged on a thin gold foil, and the angle of their deflection was measured. Prior to this discover it was very difficult to study nuclear dynamics experimentally Charged probes such as α particles from radioactive decays could only penetrate small nuclei due to the strong Coulomb repulsion. While this problem was overcome by cyclotrons, which were able to produce high-energy beams, these were very expensive to build and operate. While this picture is clearly not the entire story, it provides a remarkably simple way to understand some basic features of nuclear physics which apply to a wide-array of nuclei
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