This text investigates the mathematical and conceptual challenges of constructing quantum field theory without relying on perturbative expansions. Franco Strocchi, a physicist with extensive experience in axiomatic field theory, provides a rigorous framework that addresses the limitations of standard Lagrangian approaches. The book argues that a non-perturbative foundation is necessary to resolve long-standing issues regarding the consistency and physical interpretation of quantum fields in various dimensions.

Experts recognize this work as a highly technical and specialized resource for researchers in mathematical physics. Readers frequently note the significant mathematical density of the prose, which requires a strong foundation in functional analysis and operator algebra.