Theories of heat as inspiration for electrodynamics: From Kelvin to QFT

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Perhaps the first use of the mathematical theory of heat to develop another theory was Thomson’s use of Fourier’s equations to formulate equations for electrostatics in the 1840s. After extracting a lesson from this historical case, I will fast forward more than a century to examine the relationship between classical statistical mechanics and QFT that is induced by analytic continuation. While there is no doubt that this mathematical relationship has been heuristically useful in guiding developments in both statistical mechanics and QFT, this is a case in which the physical interpretation of the mathematics does not carry over from one theory to the other.