First Principles
Particles from First Principles Introduction The idea behind the following is to put the discrete indices on the same footing as the continuous variables. With nothing more complicated than momentum conservation and charge conservation we shall attempt to deduce the Standard Model. Definitions Let define a field Φ ( k , N ) where k is a 4-vector of continuous values and N is a vector of discrete values of unknown (or even infinite) length. k shall be called the momentum vector and N shall be called the charge vector. The vectors N could, for example, be vertices on a polytope or lattice with the property that each vector is the sum of at least one pair of other vectors. Neutral Fields Now we must also define some more (vector) functions at the special points where k =0 or N =0. Where there is no momentum of no-charge. The neutral fields are given by the Z functions, which can be contracted with a charge: Z ( k , 0 ). N The sigma functions are given by the