The method of characteristics is used to construct the fundamental solution to a system of second‐order partial differential equations. Conditions that the coefficients have to satisfy to preserve the hyperbolicity are determined and the influence of lower‐order terms is indicated. As an example, the Proca wave equation in an external field is analyzed.
REFERENCES
1.
R. Courant and D. Hilbert, Methods of Mathematical Physics (Wiley, New York, 1962), Vol. 2, p. 551.
2.
L. Garding, in Invariant Wave Equations, Proceedings of the “Ettore Majorana” International School of Mathematical Physics, Erice, Italy, 1977, Lecture Notes in Physics, Vol. 73, edited by G. Velo and A. S. Wightman (Springer, New York, 1978), p. 102.
3.
4.
J. Bjorken and S. Drell, Relativistic Quantum Fields (McGraw-Hill, New York, 1965).
5.
This section is essentially a further development of a paper by the author;
T.
Darkhosh
, J. Math. Phys.
20
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).6.
See Courant and Hilbert, Vol. 2, 626–627.
7.
8.
9.
Velo and Zwanziger, Ref. 3, Appendix A.
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© 1991 American Institute of Physics.
1991
American Institute of Physics
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