Calculation of the Wigner angle by means of vectors

Authors

DOI:

https://doi.org/10.31349/RevMexFisE.22.020201

Keywords:

Lorentz transformations; Wigner angle; light aberration

Abstract

It is shown that each Lorentz transformation leaving invariant one spatial axis can be represented by a single complex vector. This fact is employed in the calculation of the Wigner angle (which arises in the composition of two boosts in arbitrary directions) and of the aberration of light.

References

P.K. Aravind, The Wigner angle as an anholonomy in rapidity space, Am. J. Phys. 65 (1997) 634, https://doi.org/10.1119/1.18620

J.D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1998), Sec. 11.8

W. Rindler, Relativity, Special, General, and Cosmological, 2nd ed. (Oxford University Press, Oxford, 2006)

G.F. Torres del Castillo, Application of the double numbers in the representation of the Lorentz transformations, Rev. Mex. Fís. E 20 (2023) 010204, https://doi.org/10.31349/RevMexFisE.20.010204

R. Penrose and W. Rindler, Spinors and Space-Time, Vol. 1 (Cambridge University Press, Cambridge, 1984), https://doi.org/10.1017/CBO9780511564048

G.F. Torres del Castillo, Spinors in Four-Dimensional Spaces (Springer, New York, 2010), https://doi.org/10.1007/978-0-8176-4984-5

G.F. Torres del Castillo, Spinors in three dimensions. II, Rev. Mex. Fís. 40 (1994) 195

G.F. Torres del Castillo, 3-D Spinors, Spin-Weighted Functions and their Applications (Springer, New York, 2003), Secs. 1.4, 5.2.2, 5.4, https://doi.org/10.1007/978-0-8176-8146-3

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Published

2025-07-01

How to Cite

[1]
G. F. Torres del Castillo, “Calculation of the Wigner angle by means of vectors”, Rev. Mex. Fis. E, vol. 22, no. 2 Jul-Dec, pp. 020201 1–, Jul. 2025.

Issue

Vol. 22 No. 2 Jul-Dec (2025): Revista Mexicana de Física E

Section

02 Education in Physics

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Copyright (c) 2025 G.F. Torres del Castillo

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