TY - GEN
T1 - Relativistic invariance of dispersion-relations and their associated wave-operators and Green-functions
AU - Censor, Dan
PY - 2008/12/1
Y1 - 2008/12/1
N2 - Identifying invariance properties helps in simplifying calculations and consolidating concepts. Presently the Special Relativistic invariance of dispersion relations and their associated scalar wave operators is investigated for general dispersive homogeneous linear media. Invariance properties of the four-dimensional Fouriertransform integrals is demonstrated, from which the invariance of the scalar Green-function is inferred. Dispersion relations and the associated group velocities feature in Hamiltonian ray tracing theory. The derivation of group velocities for moving media from the dispersion relation for these media at rest is discussed. It is verified that the group velocity concept is a proper velocity, satisfying the relativistic transformation formula for velocities. Conversely, if we assume the group velocity to be a true (e.g., mechanical) velocity, then it follows that the dispersion relation must be a relativistic invariant.
AB - Identifying invariance properties helps in simplifying calculations and consolidating concepts. Presently the Special Relativistic invariance of dispersion relations and their associated scalar wave operators is investigated for general dispersive homogeneous linear media. Invariance properties of the four-dimensional Fouriertransform integrals is demonstrated, from which the invariance of the scalar Green-function is inferred. Dispersion relations and the associated group velocities feature in Hamiltonian ray tracing theory. The derivation of group velocities for moving media from the dispersion relation for these media at rest is discussed. It is verified that the group velocity concept is a proper velocity, satisfying the relativistic transformation formula for velocities. Conversely, if we assume the group velocity to be a true (e.g., mechanical) velocity, then it follows that the dispersion relation must be a relativistic invariant.
KW - Electromagnetic theory
KW - Special relativity
KW - Wave propagation
UR - http://www.scopus.com/inward/record.url?scp=62749132917&partnerID=8YFLogxK
U2 - 10.1109/EEEI.2008.4736699
DO - 10.1109/EEEI.2008.4736699
M3 - Conference contribution
AN - SCOPUS:62749132917
SN - 9781424424825
T3 - IEEE Convention of Electrical and Electronics Engineers in Israel, Proceedings
SP - 255
EP - 259
BT - 2008 IEEE 25th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2008
T2 - 2008 IEEE 25th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2008
Y2 - 3 December 2008 through 5 December 2008
ER -