Noel Swanson

Nature seems to be such that we can describe it accurately with quantum theories of bosons and fermions alone, without resort to parastatistics. This has been seen as a deep mystery: paraparticles make perfect physical sense, so why don’t we see them in nature? We consider one potential answer: every paraparticle theory is physically equivalent to some theory of bosons or fermions, making the absence of paraparticles in our theories a matter of convention rather than a mysterious empirical discovery. We argue that this equivalence thesis holds in all physically admissible quantum field theories falling under the domain of the rigorous Doplicher–Haag–Roberts approach to superselection rules. Inadmissible parastatistical theories are ruled out by a locality-inspired principle we call charge recombination. 1 Introduction2 Paraparticles in Quantum Theory3 Theoretical Equivalence3.1 Field systems in algebraic quantum field theory3.2 Equivalence of field systems4 A Brief History of the Equivalence Thesis4.1 The Green decomposition4.2 Klein transformations4.3 The argument of Drühl, Haag, and Roberts4.4 The Doplicher–Roberts reconstruction theorem5 Sharpening the Thesis6 Discussion6.1 Interpretations of Quantum Mechanics6.2 Structuralism and haecceities6.3 Paraquark theories.

Candidates for fundamental physical laws rarely, if ever, employ higher than second time derivatives. Easwaran sketches an enticing story that purports to explain away this puzzling fact and thereby provides indirect evidence for a particular set of metaphysical theses used in the explanation. I object to both the scope and coherence of Easwaran's account, before going on to defend an alternative, more metaphysically deflationary explanation: in interacting Lagrangian field theories, it is either impossible or very hard to incorporate higher than second time derivatives without rendering the vacuum state unstable. The so-called Ostrogradski instability represents a powerful constraint on the construction of new field theories and supplies a novel, largely overlooked example of non-causal explanation in physics.

According to spacetime state realism, the fundamental ontology of a quantum mechanical world consists of a state-valued field evolving in four-dimensional spacetime. One chief advantage it claims over rival wave-function realist views is its natural compatibility with relativistic quantum field theory. I argue that the original density operator formulation of SSR cannot be extended to QFTs where the local observables form type III von Neumann algebras. Instead, I propose a new formulation of SSR in terms of a presheaf of local state spaces dual to the net of local observables studied by algebraic QFT. 1Introduction2Spacetime State Realism in Quantum Field Theory 2.1Equivalence thesis3Entanglement and the Type III Property 3.1No-Go Lemma 13.2No-Go Lemma 24State Space Axioms for Quantum Field Theory 4.1Revised equivalence thesis5Discussion

A major obstacle facing interpreters of quantum field theory is a proliferation of different theoretical frameworks. This article surveys three of the main available options—Lagrangian, Wightman, and algebraic QFT—and examines how they are related. Although each framework emphasizes different aspects of QFT, leading to distinct strengths and weaknesses, there is less tension between them than commonly assumed. Given the limitations of our current knowledge and the need for creative new ideas, I urge philosophers to explore puzzles, tools, and techniques from all three approaches.

The CPT theorem states that any causal, Lorentz-invariant, thermodynamically well-behaved quantum field theory must also be invariant under a reflection symmetry that reverses the direction of time, flips spatial parity, and conjugates charge. Although its physical basis remains obscure, CPT symmetry appears to be necessary in order to unify quantum mechanics with relativity. This paper attempts to decipher the physical reasoning behind proofs of the CPT theorem in algebraic quantum field theory. Ultimately, CPT symmetry is linked to a systematic reversal of the C*-algebraic Lie product that encodes the generating relationship between observables and symmetries. In any physically reasonable relativistic quantum field theory it is always possible to systematically reverse this generating relationship while preserving the dynamics, spectra, and localization properties of physical systems. Rather than the product of three separate reflections, CPT symmetry is revealed to be a single global reflection of the theory’s state space.