 The Explicit Form of the Unitary Representation of the Poincaré Group for Vector-Valued Wave Functions (Massive and Massless), with Applications to Photon Localization and Position OperatorsArkadiusz Jadczyk ()
Mathematics, 2024, vol. 12, issue 8, 1-25 Abstract: We geometrically derive the explicit form of the unitary representation of the Poincaré group for vector-valued wave functions and use it to apply speed-of-light boosts to a simple polarization basis to end up with a Hawton–Baylis photon position operator with commuting components. We give explicit formulas for other photon boost eigenmodes. We investigate the underlying affine connections on the light cone in momentum space and find that while the Pryce connection is metric semi-symmetric, the flat Hawton–Baylis connection is not semi-symmetric. Finally, we discuss the localizability of photon states on closed loops and show that photon states on the circle, both unnormalized improper states and finite-norm wave packet smeared-over washer-like regions are strictly localized not only with respect to Hawton–Baylis operators with commuting components but also with respect to the noncommutative Jauch–Piron–Amrein POV measure. Keywords: photon wave function; unitary representation; Poincaré group; boost eigenmodes; position operator; POV measure; Riemannian metric; affine connection; semi-symmetric metric connection; loop-localized photon states (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:8:p:1140-:d:1373324 Access Statistics for this article Mathematics is currently edited by Ms. Emma He More articles in Mathematics from MDPI |
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