paper

A Derivation of Vector and Momentum Matrices

arXiv:math-ph/0401002

Abstract

Given standard angular momentum and boost matrices, the commutation rules for vector and momentum matrices are solved. The resulting matrix components are displayed as detailed functions of spin with factors such as the square root of (2A+1). For comparison and as an alternative, Lyubarskii's formulas in terms of Clebsch-Gordan coefficients are recalled from the literature and displayed. A set of these momentum matrices combined with the corresponding set of six angular momentum and boost matrices form the generators of a nonunitary finite dimensional representation of the Poincare group of translations, rotations and boosts. A problem set is included. PACS: 11.30.Cp Lorentz and Poincare invariance

21 pages, 9 problems. Version 3 includes Lyubarskii's vector matrix formulas so that those tempted to use the formulas derived in this article have an alternative

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