Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-02-26
Physics
High Energy Physics
High Energy Physics - Theory
6 pages, 2 figures
Scientific paper
Against the classical analysis concluding the instability of a bounded from above potential, we show that, up to two loops, the effective potential of the $\mathcal{PT}$-symmetric $(-\phi^{4}) $ scalar field theory is bounded from below as long as the vacuum condensate is pure imaginary. Unlike for the quantum mechanical case for the wrong sign ($-x^{4}$) potential, this is the first time for the existence of an explanation of the vacuum stability of a bounded from above scalar field potential. Although the resulting effective Hamiltonian is non-Hermitian, it is $\mathcal{PT}$-symmetric as well as well-defined on the real line. With the proof of stability and in view of our recent work of ability to cure the Unitarity and Ghost states problems associated with the non-Hermitian representation of the theory (arXiv:0810.3687), a save employment of the theory to play the role of the Higgs Mechanism in the Standard model of Particle interactions is now possible.
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