Bararontok said:
So this means that having an electromagnetic field has nothing to do with whether a particle will have an anti-particle or not because even the uncharged neutrino group has anti-particles. What then causes a particle to be an anti-particle if it does not have a charge opposite to its identical particle? Because when I looked at data sheets and compared the charged particles to their charged anti-particles the anti-particles were the same in every respect except for the polarity of their electromagnetic fields which are opposite to their counterparts.
Read this definition for antiparticle and you will see that having an opposite electric charge is a prerequisite to being an anti-particle:
http://en.wikipedia.org/wiki/Antiparticle
Additionally, you previously mentioned that weak iso-spin and weak hyper-charge can be used to tell the particle and anti-particle pairs apart and I saw the values RH and LH for the weak iso-spin and weak hyper-charge of the neutrinos so does this mean that RH and LH are used to differentiate the particles and anti-particles as opposed to only using the polarity of the electric charge to make the differentiation?
Shockingly enough, Wikipedia isn't always right, particularly about technical subjects. For instance, the article you linked claimed that all self-conjugate particles (i.e. particles that are their own anti-particle) are "Majorana particles," when, in fact, Majorana particles are specifically self-conjugate fermions.
What Wikipedia does get right is that having non-zero electric charge is not a prerequisite for having a distinct anti-particle. There may be other charges that distinguish the two states.
In the standard model of particle physics there are three forces, each of which is related to a type of charge. The strong force involves color charge, the SU(2) part of the electroweak force involves weak isospin, and the U(1) part involves hypercharge. While color charge is conserved in all interactions (much like electric charge), weak isospin and hypercharge are not, due to the spontaneous breaking of electroweak symmetry by the vacuum state of the Higgs field. However, since it is only the vacuum state of the system that breaks the symmetry, the actual dynamics of the fundamental fields must be the same as they would be were the symmetry exact. In other words, each field in the standard model has a well defined isospin and hypercharge (or, at worst, is a linear superposition of fields that each have well defined isospin and hypercharge).
The RH and LH you've seen discussed are chiral states, which is one basis we use to discuss spin. As it happens, the SU(2) part of the EW force discriminates by chirality. LH states have non-zero weak isospin, while RH states have 0. This means that normal, everyday fermions actually take their two spin states from different fundamental fields (which is a little weird, but works).
Weak isospin itself is actually a spinor-valued charge. (It doesn't have anything to do with the spin of the particles involved. It just uses the same kind of math that's involved in the description of spin.) As such, there will be two distinct isospin states, which we can think of as isospin up and isospin down. Fundamental fields that carry weak isospin, then, must come in doublets - one field with isospin up and one with isospin down. (This is generally characterized by a quantity called I_3, which takes the value 1/2 for isospin up and -1/2 for isospin down.) So, for instance, the (LH) electron neutrino is the isospin up component of a doublet which has the LH electron as the isospin down component. The LH up and down quarks form another such doublet (with the caveat that symmetry breaking generate mixing among the quarks in a way such that the physical down quark is really a superposition of the fundamental down, strange, and bottom quarks).
Hypercharge (denoted Y) is a scalar valued charge (like electric charge). For the dynamics to be consistent, the fields in an isospin doublet must have the same hypercharge as each other. And, after symmetry breaking, electric charge (in units of e) is given by Q = I_3 + Y. So, we can immediately see that, for example, the electron neutrino/LH electron doublet must have hypercharge -1/2, while the RH electron has hypercharge -1.
Under charge conjugation, I_3 and hypercharge each change sign. So, for a particle to be identical to its antiparticle requires at least one more condition than its electric charge being 0, at least in the case of a fundamental field with definite weak isospin and hypercharge.
Models in which the neutrinos are self-conjugate get around this by making the physical neutrino a superposition of a fundamental state with I_3 = 1/2 and Y=-1/2 and one with I_3=-1/2 and Y=1/2.