2016/09/30 by A. P. Balachandran
Physics and Astronomy · #gr-qc #hep-th #quant-ph
paper · pdf · doi:10.1142/s0219887817400084
26 pages, 3 figures, typos corrected
arxiv created 2017/06/20 · arxiv updated 2017/08/02
In nonrelatistic quantum mechanics, Born's principle of localistion is as follows: For a single particle, if a wave function ψK vanishes outside a spatial region K, it is said to be localised in K. In particular if a spatial region K' is disjoint from K, a wave function ψK' localised in K' is orthogonal to ψK. Such a principle of localisation does not exist compatibly with relativity and causality in quantum field theory (Newton and Wigner) or interacting point particles (Currie,Jordan and Sudarshan).It is replaced by symplectic localisation of observables as shown by Brunetti, Guido and Longo, Schroer and others. This localisation gives a simple derivation of the spin-statistics theorem and the Unruh effect, and shows how to construct quantum fields for anyons and for massless particles with `continuous' spin. This review outlines the basic principles underlying symplectic localisation and shows or mentions its deep implications. In particular, it has the potential to affect relativistic quantum information theory and black hole physics.