Abstract
Solving boundary value problems of electromagnetic fields was the historical starting point for the development of the Green’s function formalism. The person after whom these functions were named—George Green—published an essay in 1828 in which he introduced special functions to solve certain boundary value problems of the Poisson equation (Green 1850, 1852, and 1854). Unfortunately, this essay sank into oblivion shortly after its publication until it was rediscovered in 1846 by the later Lord Kelvin. In a paper, published in 1993, F. Dyson considered the invention of these functions as a methodical revolution in physics which was as important as the invention of computers in our days (Dyson 1993).
Metaphysics is the desperate attempt of the physicist to escape Faraday’s cage of rationality
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References
Abramowitz, M., Stegun, I.A. (eds.): Pocketbook of Mathematical Functions. Verlag Harri Deutsch, Thun, Frankfurt/Main (1984)
Aspect, A., Grangier, P., Roger, G.: Experimental tests of Bell’s inequality using time-varying analyzers. Phy. Rev. Lett. 49, 1804 (1982)
Bell, J.S.: On the Einstein Podolsky Rosen paradox. Physics 1, 195 (1964)
Bohr, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 38, 696 (1935)
Bohr, N.: The unity of human knowledge. In: Atomic Physics and Human Knowledge. Wiley, New York (1958)
Burkhardt, C.E., Leventhal, J.J.: Foundations of Quantum Physics. Springer, New York (2008)
Carroll, S.M.: Spacetime and Geometry: An Introduction to General Relativity. Addison-Wesley, München (2003)
Clauser, J.F., Horne, M.A., Shimony, A., Holt, R.A.: Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23 (15), 880 (1969)
Dirac, P.A.M.: The quantum theory of the electron. Roy. Soc. Proc. A 117, 610 (1928)
Duffy, D.G.: Green’s Functions with Applications. Chapman & Hall/CRC, Boca Raton/London/New York/Washington (2001)
Dyson, F.: George green and physics. Phys. World 6, 33 (1993)
Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)
Elmore, W.C., Heald, M.A.: Physics of Waves. Dover Publication, New York (1985)
Feynman, R.P.: The Character of Physical Law. MIT Press, Cambridge (1967)
Feynman, R.P., Hibbs, A.R.: Path Integrals and Quantum Mechanics. McGraw-Hill, New York (1965)
Feynman, R.P., Leighton, R.B., Sands, M.L.: The Feynman Lectures on Physics, Vol. 2. Addison-Wesley, München (1989)
Fikioris, J.G.: Singular integrals in the source region. J. Electromagn. Waves Appl. 18, 1505 (2004)
Graff, K.F.: Wave Motion in Elastic Solids. Dover Publication, New York (1991)
Green, G.: An essay on the application of mathematical analysis to the theories of electricity and magnetism. J. Reine Angewand. Math. 39, 73 (1850); 44, 356 (1852); 47, 161 (1854)
Heisenberg, W.: Die beobachtbaren Gr”o”sen in der Theorie der Elementarteilchen. Z. Phys. 120, 513 (1943)
Hilbert, D.: Die Grundlagen der Physik. Mathematische Annalen 92, 1–32 (1924)
Hilgevoord, J., Atkinson, D.: Time in Quantum Mechanics. Clarendon Press, Oxford (2011)
Hönl, H., Maue A.W., Westphal, K.: Theorie der Beugung, in Handbuch der Physik Band 25/1, S. Fl”ugge (Hrsg.). Springer, Berlin (1961)
Jönsson, C.: Elektronenninterferenzen an mehreren k”unstlich hergestellten Feinspalten. Zeitschrift f”ur Physik. 161, 454 (1961)
Johansson, H., Kosower, D.A., Larsen, K.J.: An Overview of Maximal Unitarity at Two Loops. arXiv:1212.2132v1 (2012)
Kadanoff, L.P., Baym, G.: Quantum Statistical Mechanics. W. A. Benjamin, Inc., California (1962)
Kraeft, W.-D., Kremp, D., Ebeling, W., Roepke, G.: Quantum Statistics of Charged Particle Systems. Akademie-Verlag, Berlin (1986)
Linton, C.M.: The Green’s function for the two-dimensional Helmholtz equation in periodic domains. J. Eng. Math. 33, 377 (1998)
McMullin, E.: The origin of the field concept in physics. Phys. Perspect. 4, 13 (2002)
Morse, P.M., Feshbach, H.: Methods of Theoretical Physics, Vol. 1 and 2. McGraw-Hill, New York (1953)
Morse, P.M., Uno Ingard, K.: Theoretical Acoustics. Princeton Univ. Press, Princeton (1986)
Müller-Kirsten, H.J.W.: Introduction to Quantum Mechanics: Schrödinger Equation and Path Integral. World Scientific, London (2006)
Newton, R.G.: Optical theorem and beyond. Am. J. Phys. 44, 639 (1976)
Nussenzveig, H.M.: High-frequency scattering by an impenetrable sphere. Ann. Phys. 34, 23 (1965)
Nussenzveig, H.M.: Causality and Dispersion Relations. Academic Press, New York and London (1972)
Parker, B.T., Petrosian, V.: Fokker-Planck equation of stochastic acceleration: Green’s functions and boundary conditions. Astrophys. J. 446, 699 (1995)
Rother, T., Kahnert, M.: Electromagnetic Wave Scattering on Nonspherical Particles: Basic Methodology and Simulations, 2nd. edn. Springer, Berlin/Heidelberg (2013)
Saxon, D.S.: Tensor scattering matrix for the electromagnetic field. Phys. Rev. 100, 1771 (1955)
Schroedinger, E.: Discussion of probability relations between separated systems. Proc. Camb. Phil. Soc. 31, 555 (1935)
Schwinger, J.: Quantum Mechanics: Symbolism of Atomic Measurements. Springer, Berlin/Heidelberg (2001)
Sommerfeld, A.: Partial Differential Equations in Physics. Academic Press, New York (1949)
Stumpf, H., Schuler, J.: Elektrodynamik. Verlag Vieweg, Braunschweig (1973)
Twersky, V.: On the scattering of waves by an infinite grating. IRE Trans. Antennas Propag. 4, 330 (1956)
Van Bladel, J.: Singular Electromagnetic Fields and Sources. Clarendon Press, Oxford (1991)
Wheeler, J.A.: On the mathematical description of light nuclei by the method of resonating group structure. Phys. Rev. 52, 1107 (1937)
Wladimirow, W.S.: Gleichungen der mathematischen Physik. VEB Deutscher Verlag der Wissenschaften, Berlin (1972)
Zhu, E.Y., et al.: Direct generation of polarization-entangled photon pairs in a poled fiber. Phys. Rev. Lett. 108, doi: 213902 (2012)
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Rother, T. (2017). Green’s Functions of Classical Fields. In: Green’s Functions in Classical Physics. Lecture Notes in Physics, vol 938. Springer, Cham. https://doi.org/10.1007/978-3-319-52437-5_3
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