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Strongly coupled quantum field theory

Marco Frasca
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Abstract

We analyze numerically a two-dimensional $λϕ^4$ theory showing that in the limit of a strong coupling $λ\to\infty$ just the homogeneous solutions for time evolution are relevant in agreement with the duality principle in perturbation theory as presented in [M.Frasca, Phys. Rev. A {\bf 58}, 3439 (1998)], being negligible the contribution of the spatial varying parts of the dynamical equations. A consequence is that the Green function method works for this non-linear problem in the large coupling limit as in a linear theory. A numerical proof is given for this. With these results at hand, we built a strongly coupled quantum field theory for a $λϕ^4$ interacting field computing the first order correction to the generating functional. Mass spectrum of the theory is obtained turning out to be that of a harmonic oscillator with no dependence on the dimensionality of spacetime. The agreement with the Lehmann-Källen representation of the perturbation series is then shown at the first order.

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Marco Frasca. 2006-01-26. Strongly coupled quantum field theory. https://doi.org/10.1103/physrevd.73.027701%2010.1103%2Fphysrevd.73.049902

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