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Date: 27-11-2018
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Date: 24-10-2018
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Date: 23-11-2018
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Any pair of equations giving the real part of a function as an integral of its imaginary part and the imaginary part as an integral of its real part. Dispersion relationships imply causality in physics. Let
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(1) |
then
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(2) |
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(3) |
where denotes the Cauchy principal value and
and
are Hilbert transforms of each other. If the complex function is symmetric such that
, then
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(4) |
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(5) |
REFERENCES:
Byron, F. W. Jr. and Fuller, R. W. Mathematics of Classical and Quantum Physics. New York: Dover, p. 344, 1992.
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