Specified finite spatial compact U(1) gauge regulator

Adopt as one selected regulated physical model the finite oriented-graph data of Exact compact U(1) rotor plus finite CAR data, with finite nonempty vertex and link sets, compact $U(1)$ rotor variables on links, finite CAR matter at vertices, fixed integer background $b_x\in \{0,\dots ,s\}$, and the displayed Gauss operators. The mathematical definition specifies ${\mathcal{H}}_{\mathrm{k}\mathrm{i}\mathrm{n}}=L^2({\mathbb{T}}^E)\widehat{\otimes }{\mathcal{F}}_a({\mathbb{C}}^{s\mathrm{\mid }V\mathrm{\mid }})$, the integer-spectrum electric operators $E_e$, link unitaries $U_e$, and the Hamiltonian $H=H_0+V_B+V_F$ on its stated maximal domain $D(H_0)$. This physical adoption does not add an embedding of the graph into space or alter the mathematical definition's operator domains.

For the physical-unit assignment, the link angles, $E_e$, $U_e$, and finite CAR operators are dimensionless. Assign units joules to ${\lambda }_E$, every ${\lambda }_p$, and every entry of $M_x$ and $T_e$ in the displayed Hamiltonian; then $H$ has units joules and $tH\mathrm{/}\mathrm{\hslash }$ is dimensionless with $t$ in seconds and $\mathrm{\hslash }$ in joule-seconds, as in Quantum field quantities and compatible SI normalizations. The graph is finite regulator data, not a coordinate lattice with an assigned spacing.

The adopted reading is limited to a model whose mathematical data are actually constructed, consistent with Physical interpretation of a supplied constructed quantum model. The CAR construction inside Exact compact U(1) rotor plus finite CAR data is conditional on Countable Choice and its inspected draft Fock/CAR supplier interfaces; this postulate does not confer proof acceptance on those carriers. It adopts no experimental result, measurement probability, continuum approximation, Lorentz-invariant continuum theory, or claim that the model describes nature.