Abstract
We shall present here some attempts to analyze quantum field theory (QFT) nonperturbatively. The main tool in this is a partially summed up and supposedly convergent version of Wilson operator product expansions on the vacuum. For realistic quantum field theory with mass and without conformal symmetry we conjecture that they are true. For conformal invariant theories we are able to prove that they hold, given only the existence of Wilson expansions as asymptotic expansions at short distances. Given these vacuum expansions (as we shall call them), arbitrary n-point Wightman functions can also be expanded; the expansion is completely fixed if all the two and three point functions of all the fields (including composite ones) in the theory are known. Given that these two and three point functions satisfy the axioms themselves, the expansion formula provides an Ansatz which satisfies all the Wightman axioms automatically if it converges, except locality. The locality constraint amounts to a crossing relation for the four point functions.
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References
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Mack, G. (1977). Conformal Invariant Quantum Field Theory. In: Lévy, M., Mitter, P. (eds) New Developments in Quantum Field Theory and Statistical Mechanics Cargèse 1976. Nato Advanced Study Institutes Series, vol 26. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-8918-1_10
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DOI: https://doi.org/10.1007/978-1-4615-8918-1_10
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