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Scalar field theory in 3+1 dimensions

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We study the existence of a stable ground state for the most general renormalizable single scalar field theory in four dimensions within a variational approach. In its regularized version we find a theory with an energy density which is not bound from below but with a metastable local minimum such that when the cutoff is removed the theory is interacting, finite, and possesses a stable ground state. In fact, we find that this theory is not stable unless it is symmetric. This generalizes Stevenson’s recent results on even φ 4 theory.

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KONIUK, R. and TARRACH, R. Scalar field theory in 3+1 dimensions. Physical Review D. 1985. Vol. 31, num. 12, pags. 3178-3182. ISSN 0556-2821. [consulted: 1 of June of 2026]. Available at: https://hdl.handle.net/2445/12434

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