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Complex structure and the construction of the $:ϕ^4_4:$ quantum field theory in four-dimensional space-time

Edward P. Osipov
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Abstract

We announce results about the nonperturbative mathematically rigorous construction of the $:\!ϕ^4_4\!:$ quantum field theory in four-dimensional space-time. The complex structure of solutions of the classical nonlinear (real-valued) wave equation and quantization are closely connected among themselves and allow to construct non-perturbatively the quantum field theory with interaction $:\!ϕ^4_4\!:$ in four-dimensional space-time. We consider vacuum averages, in particular, we construct Wightman functions and matrix elements of the scattering operator as generalized functions for finite energies. The constructed theory is obviously nontrivial.

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Edward P. Osipov. 1996-05-22. Complex structure and the construction of the $:ϕ^4_4:$ quantum field theory in four-dimensional space-time. https://arxiv.org/abs/hep-th/9605165

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