[kenhikage (OP)]

In layman's terms, can you describe spin? I know that particles with integer spin are bosons and those with half integer spin are fermions, but why? And why only integer and half integer?

[Soul Surfer]

Spin has two important aspects.  It is basically the fact that the "particle" is not a featureless symmetrical sphere but can look different from different directions.  This property was first detected in electrons.  A beam of electrons can be separated int two beams using a powerful magnetic field gradient (the Stern Gerlach experiment)  This means that the electron has got a magnetic moment as if it was a moving charge even though it is a "point" particle it was a bit like having the charge at one spot on the equator of a spinning sphere.   This is why it was initially called spin.  Later experiments showed this quantum property was more complex than this and that "spin"  could take on a range of values  0, ±1/2, 1, ±3/2, 2   and was more complex than this.  The way simple and particles behave collectively is also dependant on the total spin of the particle.

Half integer spin particle tend to insist on their own space and always occupy their own individual quantum states  (Fermi Dirac statistics)  integer spins can overlap and occupy the same quantum state  (Bose Einstein statistics).

Composite particles  protons, nuclei, atoms have a residual spin based on the sum of their component spins and this affects their collective properties.  Fermions tend to pair up and cancel out their spins but the residual half integer spins have an important effect on the properties of the substance.

[Ron Hughes]

The electron is considered a point particle, does that mean the flux density can approach infinity as we get closer and closer to it?

[imatfaal]

Not sure how you deal with surface integrals and point particles.  Will have a think - and when that does no good will try and look it up

[Soul Surfer]

Ron  Yes that's why it is probably not a complete theory.  however you have to remember like any massive particle the "size" of the particle is related to its DeBrogle wavelength this is a function of its mass and velocity (momentum) so the lower the energy the bigger it is.

imatfaal thats what "renormalisation" does to the equations  it is quite possible for functions with a pole (value of infinity at one point) in them to have a finite integral.