The Lorentz group and linear fractional transformations of the complex plane
https://doi.org/10.18384/2949-5067-2023-3-57-69
Abstract
Aim. Demonstration of the relationship between the linear-fractional function, analyzed by students of technical universities in the course of complex function theory, and the Lorentz group, which students study in the course of theoretical physics.
Methodology. Demonstration of the relationship between the fractional linear function, which is analyzed by students of technical universities in the course "Theory of Function of Complex Variable (TFCV)", and the Lorentz group, which students study in the course of theoretical physics.
Results. The one-to-one correspondence between the classes of fractional-linear transformations of the extended complex plane and the corresponding Lorentz transformations of inertial frames of reference is described in an explicit form. Physically significant examples of light aberration and Wigner rotation are described.
Research implications. The necessity of taking into account the interdisciplinary connections of theoretical physics and "Theory of Function of Complex Variable (TFCV)" in the study of the foundations of the special theory of relativity is demonstrated.
About the Authors
V. Trishin
Bauman Moscow State Technical University
Russian Federation
Russian Federation
Vladimir N. Trishin, Cand. Sci. (Phys.-Math.), Assoc. Prof.
Department of Computational Mathematics and Mathematical Physics
105005
ulitsa 2-ya Baumanskaya 5 build. 1
Moscow
N. Trishina
Bauman Moscow State Technical University; Mendeleev University of Chemical Technology of Russia
Russian Federation
Russian Federation
Natalia E. Trishina, Cand. Sci. (Phys.-Math.), Assoc. Prof., College Assoc. Prof.
Department of Computational Mathematics and Mathematical Physics
105005
ulitsa 2-ya Baumanskaya 5 build. 1
High Chemical College
125047
Miusskaya ploshad 9
Moscow
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