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INS seminars 43: Wave, Huygens principle and Green’s function (De-Chang Dai, Nov.13, 2012)

INS seminars 43

Title: Wave, Huygens principle and Green’s function

Speaker: De-Chang Dai, Institute of Natural Sciences, Shanghai Jiao Tong University

Time and place: 4:00-5:00pm, Nov 13 (Tuesday), 601 Pao Yue-Kong Library

Abstract:

It is well known that Huygens' principle is violated in an odd dimensional space time. However, the real reason of this violation is unknown. In this talk we show that the odd dimensional Green's functions do not satisfy the wave equation precisely. It could contain scalar charges which move at the speed of light. Unlike a vector charges, a moving scalar charge does not satisfy Lorentz invariance and is contracted by a \sqrt{1-v^2} factor. If a scalar charge is moving at the speed of light, its total charge is zero in the observer's frame. We also study the retarded potential solution of a scalar field in curved space-time. It is shown that gravity can affect the propagation of the scalar field in a non-trivial way.