English

Nonuniqueness of the $\lambda\Phi^4$-vacuum

High Energy Physics - Theory 2007-05-23 v3

Abstract

We prove that the massless neutral λΦ4\lambda\Phi^4-theory does not possess a unique vacuum. Based on the Wightman axioms the non-existence of a state which preserves Poincar{\'e} and scale invariance is demonstrated non-perturbatively for a non-vanishing self-interaction. We conclude that it is necessary to break the scale invariance in order to define a vacuum state. The renormalized vacuum expectation value of the energy-momentum tensor is derived from the two-point Wightman function employing the point-splitting technique and its relation to the phionic and the scalar condensate is addressed. Possible implications to other self-interacting field theories and to different approaches in quantum field theory are pointed out. PACS: 11.10.Cd, 11.15.Tk, 11.30.Qc

Cite

@article{arxiv.hep-th/0002095,
  title  = {Nonuniqueness of the $\lambda\Phi^4$-vacuum},
  author = {Ralf Schützhold and Ralf Kuhn and Michael Meyer-Hermann and Günter Plunien and Gerhard Soff},
  journal= {arXiv preprint arXiv:hep-th/0002095},
  year   = {2007}
}

Comments

10 pages in REVTeX

R2 v1 2026-07-22T14:56:41.790Z