Steps towards the axiomatic foundations of the relativistic quantum field theory: Spin-statistics, commutation relations, and CPT theorems (Q1768337)

This paper presents a new axiomatic approach to physically realistic relativistic quantum field theories. The axioms adopted there postulate about 1) a rigged Hilbert space \( {\mathcal H}_E \) as the space of states; 2) representations of the Poincaré group, space inversion, charge conjugation, time reversal as well as gauge transformations on \({\mathcal H}_E \); 3) field operators and local Lagrange operator and their transformation laws under the transformations in 2); 4) stationary action principle. From these axioms, the spin-statistics relation, the commutation relations between field operators (which are not assumed in the axioms) and the CPT theorem are proved.