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An Alternative Approach to Commutation Relations Associated with Particles of Higher Spin
Author(s) -
Lovelock D.
Publication year - 1967
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19674740503
Subject(s) - physics , rest (music) , dirac equation , spin (aerodynamics) , dirac (video compression format) , commutation , mathematical physics , quantum mechanics , rest frame , theoretical physics , quantum electrodynamics , thermodynamics , redshift , voltage , galaxy , acoustics , neutrino
Starting from a purely classical (relativistic) theory it is possible to develop a quantisation scheme which automatically gives rise to the relativistic wave equation, the usual spin operators and a condition (I) on certain operators. By demanding that this wave equation characterises particles with unique rest mass values, a second set of conditions (II) is derived, depending on an integral parameter n. From I and II the relations which constitute the Dirac electron and Kemmer meson theories are obtained in full by choosing n = 2 and n = 3 respectively. In the present note we consider the consequences of invoking the requirement that the wave equation characterises particles with several distinct rest mass values instead of unique rest mass values. A third set of conditions (III) is then deduced (which are to replace II) and these also depend on an integral parameter n. From I and III the MADHAVA RAO commutation relations for particles of spin ± 3/2ħ and ±2ħ are then derived by choosing n = 4 and n = 5 respectively. In addition the rest mass values deduced by BHABHA from an alternative viewpoint arise quite naturally.