Particles

Matter is made up of several sorts of particles, which may be elementary or composite. A proper description of particles in quantum mechanics requires relativistic field theories which are beyond the ambit of this course. We will assume that a particle can be described by a wave function of some sort.

Particles are distinguished by a number of characteristics most of which which derive from the conservation laws. These give us a set of quantum numbers with which to label states. All particles of the same type are, of course, identical and indistinguishable in quantum mechanics.

Mass

Each type of particle has a characteristic mass. This will usually be given in MeV, i.e. in terms of the energy corresponding to the invariant mass (``rest mass'') of the particle.

Lifetime

Particles can either be stable against decay into lighter particles, or unstable. In the latter case they will have a characteristic lifetime. (Note that the term stable particles sometimes means `stable against strong decays', and may include weakly decaying particles). The proton and electron are stable particles. The free neutron will decay by the weak interaction with a mean life of s.

Charge

The charge is also characteristic: it is usually expressed in units of the (absolute value of the) electron charge.

Spin

Particles may have an intrinsic spin or angular momentum. This is usually expressed in terms of the quantum of angular momentum .

Parity

This describes the behaviour of the wave function under inversion (reflection) of the coordinate axes.

Statistics

Suppose that a group of N similar (indistinguishable) particles is described by a wave function . Interchanging the ith and jth particle using some operator P leads to the new wave function . Applying P again results in the original wave function, i.e. where I is the identity (unit) operator. Hence the eigenvalues of P are .

The eigenvalue is characteristic of the particle: particles with eigenvalue +1 are known as bosons and those with -1 are known as fermions. Their group behaviour is very different. In particular two fermions cannot exist in the same state. (Suppose that the ith and jth particles above were in the same state. Then after exchange the wave function must be the same. But it must also change sign. The only consistent possibility is that it vanishes.) This is known as the Pauli exclusion principle.

This behaviour has a direct link with the spin of a particle. All particles with integer spin ( ) are bosons and those with half-integer spin ( ) are fermions.

The things we generally describe as particles are fermions. These include the quarks, the nucleons, the electron and the neutrino. Of course, these are described by quantum fields, but we consider them to be the analogues of classical particles. The things that in classical physics would be fields appear as bosons: these include the photon as the quantum manifestation of the electromagnetic field. The bosons and fermions interact, the bosons providing the `force' between fermions.

In quantum field theory, fermions are created from the vacuum in pairs: energy is shared between the particles. Particles in the pair have the same masses but opposite charges and other quantum numbers. The pair can be regarded as a particle and its antiparticle. Thus each type of fermionic particle is `mirrored' by a corresponding antiparticle. The minimum energy required to create a pair is where m is the invariant mass of the particle. An example is the creation of an electron-positron pair by a gamma ray in the field of a nucleus.