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

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

1996-05-22

arxiv.org/abs/hep-th/9605165v1

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, LaTeX

Scientific paper

We announce results about the nonperturbative mathematically rigorous construction of the $:\!\phi^4_4\!:$ 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 $:\!\phi^4_4\!:$ 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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