Pragmatists and Purists on CPT Invariance in Relativistic Quantum Field Theories

Pragmatist approaches to relativistic quantum field theories (RQFTs) trade mathematical rigor for the ability to derive predictions from realistic interacting theories. Examples include the Lagrangian approach found in most textbooks, and Weinberg’s approach. Purist approaches to RQFTs trade the ability to formulate realistic interacting theories for mathematical rigor. Examples include the axiomatic and algebraic formalisms. Philosophers are split on whether foundational issues related to RQFTs should be framed within pragmatist or purist approaches.Wallace (2011), for instance, has argued that cutoff quantum field theory (CQFT), a particular pragmatist approach, has been successful at resolving the problems associated with renormalized perturbation theory, while axiomatic and algebraic quantum field theory (AQFT), which epitomize purist approaches, have not; and this indicates that CQFT is the correct framework for philosophy of QFT. Fraser (2011), on the other hand, argues that renormalization techniques indicate how CQFT and AQFT are empirically indistinguishable, and that AQFT is to be preferred for its mathematical rigor. This essay probes this debate by viewing it through the lens of the CPT theorem. This theorem entails that the state of a physical system described by an RQFT must possess CPT invariance; i.e., invariance under the combined transformations of charge conjugation C, space inversion P, and time reflection T. There are both pragmatist and purist versions of this theorem (Bain 2013). While all versions apply unproblematically to non-interacting states, and some unrealistic interacting states,