The Electromagnetic Field

The electromagnetic field is a gauge group U(1). For the purpose of our approach it is useful to describe the EM charge as a combination of two different charges:

• The baryon charge I_B distinguishes quarks from leptons. It is 1/3 for each quark, so that three quarks give a baryon with baryon charge 1). It is constant on doublets, similar to the colors of the quarks. A gauge group with this charge would form, together with the color group SU(3), the group U(3). (The group U(3) is a little bit easier to define than SU(3), in correspondence with the shorter denotation.)
• The shifted isospin charge I₃-1/2 has the values 0 and -1 inside the electroweak doublets. This charge is defined in the same way on all doublets, independent of their generation, color, or baryon charge. This characterization makes it close to the weak interactions.

The EM charge Q is, now, a simple linear combination of these two charges:

Q = 2 I_B + (I₃-¹⁄₂)

The point of this decomposition is that the two parts appear in a different way in our model:

• The first part, 2 I_B, fits into the scheme of Wilson gauge fields.
• The second part, (I₃-1/2), fits into the scheme of gauge-like fields describing lattice deformations.