Abstract: While one might hope that the transition from quantum mechanics to quantum field theory preserves an intuitive picture of localised physical entities, this expectation quickly breaks down. In relativistic quantum field theory, the notion of a spatially localised particle is far from straightforward. The standard construction proceeds by selecting a positive-frequency subspace of classical solutions to ensure a Hamiltonian bounded from below. However, within this framework, there is no well-defined position operator with sharply localised eigenstates; at best, one obtains unsharp or approximately localised states. This undermines the familiar quantum-mechanical picture of particles as entities with definite spatial localisation.
This motivates alternative localisation schemes, most notably the Newton–Wigner (NW) construction, which restores a sharp notion of position. NW localisation provides well-defined position operators and localised states, but this comes with significant costs: it is frame-dependent, fails to transform covariantly under Lorentz boosts, and permits superluminal propagation. As such, it sits uneasily with the relativistic structure that quantum field theory is meant to respect.
The tension between these schemes reflects a deeper question about the ontology of quantum field theory: how, if at all, should we understand observables associated with a spacetime region O? In this talk, I will compare the field and NW localisation as competing schemes that encode different physical priorities. I will argue that the failure of NW localisation to respect microcausality undermines its candidacy as a fundamental localisation scheme. Instead, we should accept field localisation while revising our expectations of local operations.
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Philosophy of Physics Graduate Lunch Seminar Convenors: Paolo Faglia, Gregor Gajic and Rachel Pederson
