A general method of calculating the retarded and advanced Green’s functions for the second order hyperbolic partial differential equations in the neighborhood of the characteristic surfaces is developed. This method is then applied to two examples: the Proca wave equation in an external electromagnetic field and the Proca wave equation in an external symmetrical tensor field. The second example is of special interest since it exhibits acausal behavior. For this case, it is shown that the field commutators do not vanish for all spacelike separations and that the commutator of the energy tensor with itself is nonzero in the region bounded by the light cone and the spacelike characteristic surface.
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© 1979 American Institute of Physics.
1979
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