Factorization of the Lorentz Transformations

Authors

  • K.S. Karplyuk Taras Shevchenko National University of Kyiv
  • M.I. Kozak Uzhhorod National University, Department of Physics
  • O.O. Zhmudskyy University of Central Florida

DOI:

https://doi.org/10.15407/ujpe68.1.19

Keywords:

hypercomplex numbers, Lorentz group

Abstract

The article shows how the factorization of an arbitrary Lorentz transformation is performed. That is, the representation of an arbitrary Lorentz transformation as a sequence of a spatial rotation and a boost or a boost and a spatial rotation. Relations are obtained that determine the required boosts and turns.

References

J.D. Bjorken S.D. Drell. Relativistic Quantum Mechanics (Mc-Graw Hill Book Company, 1964).

G. Casanova. Lalgebre Vectorielle (Presses Universitaires de France, 1976).

A.V. Berezin, Yu.A. Kurotchkin, E.A. Tolkatchev. Quaternions in Relativistic Physics (Sci. and Technol., 1989) (in Russian).

F.I. Fedorov. Lorentz Group (Nauka, 1979).

K. Karplyuk, O. Zhmudskyy. The hypercomplex solution of the Dirac equation. Universal J. Phys. Appl. 1 (1), 1 (2013).

https://doi.org/10.13189/ujpa.2013.010101

K. Karplyuk, O. Zhmudskyy. The hypercomplex equations for fermion interaction description. J. Mod. Phys. 1 (3), 24 (2014).

https://doi.org/10.15764/MPHY.2014.03004

N.N. Bogoliubov D.V. Shirkov. Introduction to the Theory of Quantized Fields (John Wiley & Sons, 1980).

S.S. Schweber. An Introduction to Relativistic Quantum Field Theory (Row, Peterson and Co, Evanston, Ill., Elmsford, 1961).

A.V. Berezin, Yu.A. Kurotchkin, E.A. Tolkatchev. Quaternions in Relativistic Physics (Sci. and Technol, 1989) (in Russian).

V. Fock. The Theory of Space, Time and Gravitation (Pergamon Press, 1959).

K. Karplyuk, O. Zhmudskyy. On calculation of amplitudes in quantum electrodynamics. Phys. Rev. D 86, 015015 (2012).

https://doi.org/10.1103/PhysRevD.86.015015

L.H. Thomas. I. The kinematics of an electron with an axis. Philosophical Magazine 3 (7), 1 (1927).

https://doi.org/10.1080/14786440108564170

K. Karplyuk, O. Zhmudskyy. The universal expression for the amplitude square in quantum electrodynamics. J. Modern Phys. 6 (15), 2219 (2015).

https://doi.org/10.4236/jmp.2015.615226

J.K. Lubanski. Sur la th'erie des particules 'el'ementaires de spin quelconque. II. Phisica (in French) 9, 310 (1942).

https://doi.org/10.1016/S0031-8914(42)90113-7

K. Karplyuk. On the description of vector Bosons. Universal J. Phys. Appl. 1 (1), 14 (2013).

https://doi.org/10.13189/ujpa.2013.010103

E.P. Wigner. On unitary representations of the inhomogeneous Lorentz group. Ann. Math. 40, 149 (1939).

https://doi.org/10.2307/1968551

Downloads

Published

2023-03-12

How to Cite

Karplyuk, K., Kozak, M., & Zhmudskyy, O. (2023). Factorization of the Lorentz Transformations. Ukrainian Journal of Physics, 68(1), 19. https://doi.org/10.15407/ujpe68.1.19

Issue

Section

General physics