(Material comes from Introduction to Elementary Particles by Griffiths, Introduction.

Introduction

What is Elementary Particle Physics?

Since at least the time of the Greek philosopher Democritus, one aspect of physics has been the goal of finding the most basic constituents of objects, organisms, and the world. In our time, this goal has led to the discovery of the electron, proton, neutron, photon, and a host of other objects. Elementary particle physics is the study of the basic constituents of our world and their interactions.

indistinguishable particles

particle properties: mass, charge, spin, C, P, ...

How is it possible to study the interactions between particles. To study the electrostatic repulsion between two charged non-conducting spheres, we can hang them from non-conducting strings and measure the force one sphere produces on the other. But we can't "pick up" an electron, let alone attach it to a string, so how do we study it's interactions?

We have to resort to less direct means to probe the interactions of elementary particles. The various methods basically fall into one of three categories:

scattering events, where we shoot one particle at another and observe the particles that emerge afterward,
decays, where a particle spontaneously disintegrates and we observe the debris, and
bound states, where we measure the properties of the composite object formed when two or more constituents stick together.

These methods have the advantage of being experimentally feasible, but do take us further from the basic interactions we wish to investigate. Extracting information about the interaction from such measurements is not a trivial task. The process often involves extensive simulation of the experiment, and comparison of the simulation with the observed results.

What are the ingredients needed for a theory of elementary particles? The microscopic size of the particles might lead you to guess (correctly) that quantum mechanics is needed. For elementary particles, it is often the case that their kinetic energy is comparable to their (rest) mass. In other words, they usually move at speeds close to the speed of light, where special relativity is required. The marriage of quantum mechanics and special relativity was originally accomplished by Paul A.M. Dirac. The results of his work lead to quantum field theory.

Note the difference between a type of mechanics and a particular force law. Quantum field theory describes the mechanics of particle interactions, and the goal is to understand the "force law" that correctly describes the behavior.

We will often deal with situations where the details of the interaction are unimportant. For instance, given a decay such as D⁰ to K^-π⁺, we can determine the energy and momentum of the outgoing particles using conservation of energy and momentum in the context of relativistic kinematics.

The D⁰ decays to many other final states as well. When we have a quantum mechanical state that can decay to a number of final states, then each of the possible transitions has a certain probability. We can't say with certainty which final state a particular particle will decay to, but we can determine the probability.

The union of special relativity with quantum mechanics brings additional results:

anti-particles
Pauli exclusion
CPT theorem

The theory that we now have that describes the known particles and their interactions is called the Standard Model of particle physics.