III The Standard Model - Introduction

0Introduction

III The Standard Model

0 Introduction

In the Michaelmas Quantum Field Theory course, we studied the general theory

of quantum field theory. At the end of the course, we had a glimpse of quantum

electrodynamics (QED), which was an example of a quantum field theory that

described electromagnetic interactions. QED was a massively successful theory

that explained experimental phenomena involving electromagnetism to a very

high accuracy.

But of course, that is far from being a “complete” description of the universe.

It does not tell us what “matter” is actually made up of, and also all sorts of other

interactions that exist in the universe. For example, the atomic nucleus contains

positively-charged protons and neutral neutrons. From a purely electromagnetic

point of view, they should immediately blow apart. So there must be some force

that holds the particles together.

Similarly, in experiments, we observe that certain particles undergo decay.

For example, muons may decay into electrons and neutrinos. QED doesn’t

explain these phenomena as well.

As time progressed, physicists managed to put together all sorts of experi-

mental data, and came up with the Standard Model. This is the best description

of the universe we have, but it is lacking in many aspects. Most spectacularly,

it does not explain gravity at all. There are also some details not yet fully

sorted out, such as the nature of neutrinos. In this course, our objective is to

understand the standard model.

Perhaps to the disappointment of many readers, it will take us a while before

we manage to get to the actual standard model. Instead, during the first half of

the course, we are going to discuss some general theory regarding symmetries.

These are crucial to the development of the theory, as symmetry concerns impose

a lot of restriction on what our theories can be. More importantly, the “forces”

in the standard model can be (almost) completely described by the gauge group

we have, which is

(3)

× SU

(2)

U(1). Making sense of these ideas is crucial

to understanding how the standard model works.

With the machinery in place, the actual description of the Standard Model is

actually pretty short. After describing the Standard Model, we will do various

computations with it, and make some predictions. Such predictions were of course

important — it allowed us to verify that our theory is correct! Experimental

data also helps us determine the values of the constants that appear in the

theory, and our computations will help indicate how this is possible.

Historically, the standard model was of course discovered experimentally,

and a lot of the constructions and choices are motivated only by experimental

reasons. Since we are theorists, we are not going to motivate our choices by

experiments, but we will just write them down.