The Photon

The photon is the quantum of the connection. You have seen the connection derived. Now meet its minimum excitation.

The connection Aμ is a field on the manifold. When quantised (AP09 gives the quantum sector), it has excitations. The minimum excitation is one quantum: the photon.

The photon is a boson. You knew this. Now you know why. AP11 derives: paired elements (σ-image exists) are bosons, integer spin. The connection Aμ is a property of the pre-state, which has both sectors ℒ and 𝒫 (Axiom S). The phase is symmetric under σ (that is the Born rule: P = ψψ*). The quantum of a σ-symmetric field is a paired element. Paired elements are bosons. The photon is a boson.

The photon has spin 1. The connection Aμ is a 1-form: one Lorentz index. A 1-form on a 4D Lorentzian manifold transforms as a vector under the Lorentz group. The massless vector representation has spin 1. [This step uses Lorentz representation theory, which is standard mathematics on the derived manifold.]

The photon is massless. The phase symmetry is exact — U(1) is not broken. A gauge-invariant mass term m²AμAμ is forbidden by U(1) gauge invariance (this is a mathematical identity, not an assumption). If U(1) were broken, the photon would acquire mass via the Higgs mechanism; but U(1) is the phase freedom of the Born rule, which is exact (KS-5 CLOSED). The photon is massless because the Born rule is exact. If you could break the Born rule, you could give the photon mass. You cannot.

The photon propagates at c. Axiom C gives a finite causal bound. Maxwell’s equations (section 4.4, derived via Theorem 3) give a wave equation whose characteristic speed is c. A massless excitation of a field satisfying Lorentz-covariant dynamics propagates at the causal bound. This is the identification made in the corpus: c = finite causal bound (Axiom C). Light speed is not a property of light. It is a property of the connection. It is Axiom C read through the derived dynamics.