"Classical" model of discrete QFT: Klein Gordon and electromagnetic fields

Physics – General Physics

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22 pages, no figures

Scientific paper

The purpose of this paper is to propose a "classical" model which is relativistic with respect to a "superluminal" (but finite) speed $c_s$, and would result in emergent quantum field theory. This paper is exclusively devoted to the path integral representation of Klein-Gordon and Maxwell fields. The key challenge to overcome is the fact that a "path integral" is taken over an infinite-dimensional space, yet we are attempting to embed it in four dimensions for the purposes of making it ontologically meaningful. The key idea used to achieve the embedding is a discretization of infinite-dimensional space. Once the discretization is done our "infinite-dimensional" space will contain a finite number of elements, which means that "there is enough room" to embed it into four dimensions. The purpose of this paper is to specify the embedding and come up with a "classical" model that would produce a Feynman path integral in terms of the "inverse" of that embedding.

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