Summary
It is shown that every proper, complex Lorentz matrixL can be expressed in the formL=Σ exp [AG], whereA is an antisymmetric matrix,G is the metric matrix, and Σ=±l. It is then shown that not every proper, complex Lorentz matrixL can be expressed in the formL=exp [AG], withA andG as above.
Riassunto
Si dimostra che ogni matrice di Lorentz propria e oomplessa,L, puÒ essere espressa nella formaL = Σ exp [AG], doveA è una matrice antisimmetrica,G è la matrice metrica, e Σ=±1. Si dimostra poi che non tutte le matrici di Lorentz proprie e complesse,L, si possono esprimere nella formaL = exp [AG], conA eG come sopra.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
F. D. Mubnaghan:The Theory of Group Representations (Baltimore, 1938), p. 356.
V. I. Smirnov:Linear Algebra and Group Theory (New York, 1961), p. 417, problems 13, 14.
F. R. Gantmacher:Applications of the Theory of Matrices (New York, 1959), p. 14, 15, Theorem 7.
Author information
Authors and Affiliations
Additional information
The contribution of H. E. M. was made prior to his employment with Lincoln Laboratories.
Rights and permissions
About this article
Cite this article
Lomont, J.S., Moses, H.E. Exponential representation of complex Lorentz matrices. Nuovo Cim 29, 1059–1067 (1963). https://doi.org/10.1007/BF02750132
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02750132