Degrees of freedom of quantum fields and elementary particles

[Lapidus]

They say that a photon has two degrees of freedom, its two polarization states.

Does that also mean that the electron has only two degrees of freedom, its two spin states?

What about the frequency of a photon, is that not a degree of freedom? Or the three space directions that a electron can travel? What mans degree of freedom anyway when referring to elementary particles and its quantum fields?

thanks

 

[AdrianTheRock]

These degrees of freedom are those over and above those of energy/momentum. For free particles, the latter give three additional quantities (three directions of momenta plus the total energy but minus one because of the relationship between total energy, total momentum and the particle's mass).

An electon does also have only two possible spin states, though this arises from different equations than those which govern photons. By contrast, W and Z bosons each have three polarisation states as they are massive.

In general the degrees of freedom correspond to whatever quantum numbers the particle has. In some cases this depends on what you define as being the 'same' particle. For example, if you define an up quark generically as a single particle then it has three colour states, whereas if you define u_R, u_B and u_G as separate particles then obviously they don't indiviudally have that particular freedom. The former approach itends to be used when considering symmetries, particularly unbroken ones such as the colour states of quarks or spin polarisations. It's important to be clear what one is doing.