Identical Particles and Statistics in Superselection Theory

Regents Of The University Of Michigan - Ann Arbor, Ann Arbor MI

Investigators

Abstract

Identical quantum particles (such as Fermions and Bosons) have intriguing statistical properties (Bose statistics and Fermi statistics) that raise serious issues for naive philosophical accounts of identity. The predominant context for interpretive studies of identical particles has been basic quantum mechanics. The PIs propose to develop an interpretive study in the context of quantum field theory, which is more fundamental. The study involves a theory of superselection developed in the algebraic formulation of quantum field theory by Doplicher, Haag, and Roberts. The theory provides a mathematical explaination of superselection, which would otherwise be a postulated set of rules that forbid the preparation of a superposition of states associated with different types of identical particles. They plan to focus attention on two research questions. The first concerns whether superselection theory (in the algebraic formulation of quantum field theory) provides a more fundamental explanation for why systems obey Bose rather than Fermi statistics (for example). The second addresses how scientific results involving identical particles are to be understood in quantum field theory, in light of powerful arguments against the existence of particles. Intellectual Merit. This project will bring the philosophy of quantum field theory into contact with long-standing problems in the philosophy of quantum mechanics. Quantum field theory has been the source of many novel conceptual problems, particularly (though not solely) having to do with the existence of unitarily inequivalent representations of the theory. This has led to much fruitful research, but also to a lack of engagement between philosophy of quantum field theory and work on quantum mechanics, even in areas where the study of quantum field theory should bear on the older debates. The metaphysics of statistics is one such largely-neglected area. Broader Impacts This is a deeply interdisciplinary project that brings together aspects of philosophy, modern physics, and mathematics. It proceeds in a spirit of cooperative (rather than critical) exchange between these fields, and it will contribute to enhancing constructive developments at some crucial points of contact between science and philosophy of science. The results of this project will prove to be of interest to mathematicians, physicists, and philosophers of science. The project also integrates teaching and research; the senior researcher plans to teach a graduate seminar on the subject matter of the project; the junior researcher will participate in teaching the course.