The Position Operator Revisited Annales De L’I

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ANNALES DE L’I. H. P., SECTION A H. BACRY The position operator revisited Annales de l’I. H. P., section A, tome 49, no 2 (1988), p. 245-255 <http://www.numdam.org/item?id=AIHPA_1988__49_2_245_0> © Gauthier-Villars, 1988, tous droits réservés. L’accès aux archives de la revue « Annales de l’I. H. P., section A » implique l’accord avec les conditions générales d’utilisation (http://www.numdam. org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce ﬁchier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ .

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Rotation and Spin and Position Operators in Relativistic Gravity and Quantum Electrodynamics
Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 4 December 2019 doi:10.20944/preprints201912.0044.v1 Peer-reviewed version available at Universe 2020, 6, 24; doi:10.3390/universe6020024 1 Review 2 Rotation and Spin and Position Operators in 3 Relativistic Gravity and Quantum Electrodynamics 4 R.F. O’Connell 5 Department of Physics and Astronomy, Louisiana State University; Baton Rouge, LA 70803-4001, USA 6 Correspondence: [email protected]; 225-578-6848 7 Abstract: First, we examine how spin is treated in special relativity and the necessity of introducing 8 spin supplementary conditions (SSC) and how they are related to the choice of a center-of-mass of a 9 spinning particle. Next, we discuss quantum electrodynamics and the Foldy-Wouthuysen 10 transformation which we note is a position operator identical to the Pryce-Newton-Wigner position 11 operator. The classical version of the operators are shown to be essential for the treatment of 12 classical relativistic particles in general relativity, of special interest being the case of binary 13 systems (black holes/neutron stars) which emit gravitational radiation. 14 Keywords: rotation; spin; position operators 15 16 I.Introduction 17 Rotation effects in relativistic systems involve many new concepts not needed in 18 non-relativistic classical physics. Some of these are quantum mechanical (where the emphasis is on 19 “spin”). Thus, our emphasis will be on quantum electrodynamics (QED) and both special and 20 general relativity. Also, as in [1] , we often use “spin” in the generic sense of meaning “internal” spin 21 in the case of an elementary particle and “rotation” in the case of an elementary particle.
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