Issues

 / 

1978

 / 

July

  

Methodological notes


The four-dimensional group velocity

The advantages of using the 4-dimensional group velocity are demonstrated. After first giving its purely kinematic definition for an arbitrary wave field, the discussion turns to packets of electromagnetic waves in electrically and magnetically anisotropic media which possess space-time dispersion and are smoothly nonuniform in space and slowly varying in time. In particular, a simple expression is obtained for the energy-momentum 4-tensor in terms of the group-velocity 4-vector. Finally, it is shown how the 4-dimensional notation simplifies the derivation of the conditions of orthogonality and conservation of the adiabatic invariant. A note by M. L. Levin which follows this paper contains a brief account of the basis results of W. R. Hamilton's investigations relating to the velocity of wave motion.

PACS: 04.40.+c
DOI: 10.1070/PU1978v021n07ABEH005668
URL: https://ufn.ru/en/articles/1978/7/e/
Citation: Polevoi V G, Rytov S M "The four-dimensional group velocity" Sov. Phys. Usp. 21 630–638 (1978)
BibTexBibNote ® (generic)BibNote ® (RIS)Medline RefWorks
RT Journal
T1 The four-dimensional group velocity
A1 Polevoi,V.G.
A1 Rytov,S.M.
PB Physics-Uspekhi
PY 1978
FD 10 Jul, 1978
JF Physics-Uspekhi
JO Phys. Usp.
VO 21
IS 7
SP 630-638
DO 10.1070/PU1978v021n07ABEH005668
LK https://ufn.ru/en/articles/1978/7/e/

Оригинал: Полевой В Г, Рытов С М «О четырехмерной групповой скорости» УФН 125 549–565 (1978); DOI: 10.3367/UFNr.0125.197807f.0549

© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions