Non-perturbative foundations of quantum field theory

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This chapter discusses the physical principles that characterize a theory which combines quantum mechanics and relativity, describing particle interactions by fields: QM1, Hilbert space structure of states; QM2, energy–momentum spectral condition; QM3, field operators; R1, relativistic covariance; and R2, microcausality or locality. Such conditions (called Wightman axioms) imply corresponding properties of the vacuum expectations of the fields (Wightman functions); conversely, the latter ones fully determine a relativistic quantum mechanics (reconstruction theorem). Remarkable consequences are the analyticity properties of the Wightman functions, leading to structural information on the theory.