Quantum Field Theory Mathematics

These pages construct algebraic states, distributional test spaces, Fock conventions and free-field carriers, together with finite measurement instruments. Further topics include Clifford algebra, gauge data, soft coherent profiles, finite regulator models, polynomial functionals and scaling-degree extensions. Exact finite or regulated constructions are distinguished from formal coefficients and unconstructed limits. Every result specifies its spaces, domains, pairings and hypotheses before those objects enter the corresponding physical framework.

Each main page introduces the objects and assumptions needed for its results, with links to the prerequisites used in the exposition. Its examples companion gives concrete calculations, limiting cases or counterexamples that clarify those hypotheses. Follow prerequisite links when a definition or earlier result is needed, and read the stated scope alongside each conclusion. Local statements distinguish assumptions from deductions and keep the conventions used in calculations visible. The page list below provides entry points into the subject; the order follows the planned progression from foundational definitions to the later applications.

• Unital star algebra and positive normalized state
• Tensor test algebra and positive tempered moment data
• Finite bounded instruments normalize measurement probabilities
• Schwartz/distribution spaces and Hilbert Fock conventions
• Scalar future mass-shell measure and test restriction
• Exact massless scalar on a conformally flat external metric
• Example conventions, energy units and constructed/formal data
• Dirac Clifford matrices and energy projections
• Tempered time-ordered scalar two-point carrier
• Charged gauge data and SI-natural conventions
• Finite matrix formal inverse and gauge-covariant kernel
• Clifford traces and normalized spin completeness
• Soft-current angular norm and exact cutoff coherent model
• Ideal linear Penning mode-frequency invariant
• Exact compact U1 rotor plus finite CAR data
• Finite-lattice polynomial Hamiltonian data
• Finite Euclidean quartic interacting measure
• Regular polynomial field functional algebra
• Scaling degree and local extension space
• Finite quartic graph and superficial scaling conventions