Pct, Spin And Statistics, And All That

A. S. Wightman algebra analytic continuation anti-commute argument asymptotic completeness automorphism axioms boson field boundary value coherent subspace complex Lorentz convergence cutoff cyclic vector D₁ defined definition domain equation equivalence class even-odd rule example exists extended tube F₁ F₂ free field given Haag's theorem Hamiltonian hermitian scalar field Hilbert space holomorphic function implies interaction invariant irreducible set Jost points Klein transformation linear Lorentz group Lorentz transformation mass Math matrix monomial normal commutation relations open set orthogonal particles PCT operator PCT theorem Phys physical Poincaré polynomial proof prove Quantum Field Theory renormalization representation scalar field scalar product Section self-adjoint sequence smeared fields space-like separated space-time spinor statistics subset super-selection rules Suppose symmetry tempered distribution test functions transformation law unitary vacuum expectation values vanishes variables weakly zero