We present a unified relativistic field theory over the ring of adeles AQ, in whichthe nontrivial zeros of the Riemann zeta function emerge as quantized energy levelsof a self-adjoint Hilbert—P´olya operator ˆH. The theory begins with a Non-Hermitian"Adelic Carnot Pump" driven by local prime interactions (Cup and Cap products),Hermitianized globally through restriction to the cuspidal subspace of automorphicforms on GL2(Q)GL2(A).The Arithmetic Planck constant hA ∼ log 2 quantizes phase steps, while the weight-12 modular discriminant ∆ provides vacuum tension. Maxwell-like adelic field equa-tions govern the dynamics, culminating in a least-arithmetic-action principle whosegeodesics are confined to the critical line Re(s) = 1/2.A dimensionless Arithmetic Fine-Structure Constant αA ≈ 1/(log 2 · 2π) tunes thecoupling between local curvature and global flow. Invariance of αA under the fulladelic group action is enforced by an Arithmetic Noether Theorem, which acts as acentripetal force locking spectral ordinates to the critical line.Self-adjointness follows from cuspidal sealing and unitary Atkin—Lehner symmetry;spectral matching is achieved via a twisted trace formula that projects the GL2 cuspidalspectrum onto the GL1 zeta zeros through phase-cancellation of non-coherent modes.We conclude that the Riemann Hypothesis is the symmetry requirement for acausal, lossless arithmetic vacuum: all nontrivial zeros satisfy Re(ρ) = 1/2. Exten-sions to the Birch and Swinnerton-Dyer conjecture are suggested.Keywords: Riemann Hypothesis, Hilbert—P´olya conjecture, adelic geometry, au-tomorphic forms, Noether theorem, non-Hermitian dynamics, modular forms, criticalline1